{"id":4234,"date":"2025-06-05T05:27:26","date_gmt":"2025-06-05T05:27:26","guid":{"rendered":"https:\/\/diznr.com\/?p=4234"},"modified":"2025-06-05T05:27:26","modified_gmt":"2025-06-05T05:27:26","slug":"mathematics-short-tricks-square-tricks-and-square-root-tricks-mathematics-in","status":"publish","type":"post","link":"https:\/\/www.reilsolar.com\/pdf\/mathematics-short-tricks-square-tricks-and-square-root-tricks-mathematics-in\/","title":{"rendered":"Mathematics Short Tricks\/SQUARE TRICKS AND SQUARE ROOT TRICKS IN MATHEMATICS."},"content":{"rendered":"<p>Mathematics Short Tricks\/SQUARE TRICKS AND SQUARE ROOT TRICKS IN MATHEMATICS.<\/p>\n<p>[fvplayer id=&#8221;671&#8243;]<\/p>\n<h3 data-start=\"0\" data-end=\"62\"><strong data-start=\"2\" data-end=\"60\">Mathematics Short Tricks \u2013 Square &amp; Square Root Tricks<\/strong><\/h3>\n<p data-start=\"64\" data-end=\"271\">Learning <strong data-start=\"73\" data-end=\"106\">square and square root tricks<\/strong> helps in fast calculations, which is useful for competitive exams like SSC, Banking, GATE, and more. Below are some powerful tricks to speed up your calculations.<\/p>\n<h3 data-start=\"278\" data-end=\"337\"><strong data-start=\"281\" data-end=\"335\">\u00a0Square Tricks (\u0924\u0947\u091c\u0940 \u0938\u0947 \u0935\u0930\u094d\u0917 \u0928\u093f\u0915\u093e\u0932\u0928\u0947 \u0915\u0940 \u091f\u094d\u0930\u093f\u0915\u094d\u0938)<\/strong><\/h3>\n<h3 data-start=\"339\" data-end=\"375\"><strong data-start=\"343\" data-end=\"373\">\u00a0Any Number Ending in 5<\/strong><\/h3>\n<p data-start=\"376\" data-end=\"429\">For numbers ending in <strong data-start=\"398\" data-end=\"403\">5<\/strong>, use this simple trick:<\/p>\n<p data-start=\"431\" data-end=\"448\"><strong data-start=\"434\" data-end=\"446\">Formula:<\/strong><\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">(AB)2=A\u00d7(A+1)\u0914\u0930\u00a0\u0905\u0902\u0924\u00a0\u092e\u0947\u0902\u00a025\u00a0\u091c\u094b\u0921\u093c\u00a0\u0926\u0947\u0902\u0964(AB)^2 = A \\times (A+1) \\quad \\text{\u0914\u0930 \u0905\u0902\u0924 \u092e\u0947\u0902 25 \u091c\u094b\u0921\u093c \u0926\u0947\u0902\u0964}<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mord mathnormal\">B<\/span><span class=\"mclose\">)<span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">\u00d7<\/span><\/span><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">1<\/span><span class=\"mclose\">)<\/span><span class=\"mord text\"><span class=\"mord brahmic_fallback\">\u0914\u0930<\/span><span class=\"mord\">\u00a0<\/span><span class=\"mord brahmic_fallback\">\u0905\u0902\u0924<\/span><span class=\"mord\">\u00a0<\/span><span class=\"mord brahmic_fallback\">\u092e\u0947\u0902<\/span><span class=\"mord\">\u00a025\u00a0<\/span><span class=\"mord brahmic_fallback\">\u091c\u094b\u0921\u093c<\/span><span class=\"mord\">\u00a0<\/span><span class=\"mord brahmic_fallback\">\u0926\u0947\u0902\u0964<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p data-start=\"517\" data-end=\"545\"><strong data-start=\"520\" data-end=\"532\">Example:<\/strong> <span class=\"katex\"><span class=\"katex-mathml\">35235^2<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">3<\/span><span class=\"mord\">5<span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<ul data-start=\"546\" data-end=\"661\">\n<li data-start=\"546\" data-end=\"624\">Take <strong data-start=\"553\" data-end=\"568\">first digit<\/strong> (3) \u2192 Multiply by next number \u2192 <span class=\"katex\"><span class=\"katex-mathml\">3\u00d74=123 \\times 4 = 12<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">3<\/span><span class=\"mbin\">\u00d7<\/span><\/span><span class=\"base\"><span class=\"mord\">4<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">12<\/span><\/span><\/span><\/span><\/li>\n<li data-start=\"625\" data-end=\"661\">Add <strong data-start=\"631\" data-end=\"637\">25<\/strong> at the end \u2192 <strong data-start=\"651\" data-end=\"659\">1225<\/strong><\/li>\n<\/ul>\n<p data-start=\"663\" data-end=\"696\"><strong data-start=\"665\" data-end=\"676\">Answer:<\/strong> <span class=\"katex\"><span class=\"katex-mathml\">352=122535^2 = 1225<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">3<\/span><span class=\"mord\">5<span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">1225<\/span><\/span><\/span><\/span><\/p>\n<p data-start=\"698\" data-end=\"726\"><strong data-start=\"701\" data-end=\"713\">Example:<\/strong> <span class=\"katex\"><span class=\"katex-mathml\">75275^2<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">7<\/span><span class=\"mord\">5<span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<ul data-start=\"727\" data-end=\"775\">\n<li data-start=\"727\" data-end=\"775\"><span class=\"katex\"><span class=\"katex-mathml\">7\u00d78=567 \\times 8 = 56<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">7<\/span><span class=\"mbin\">\u00d7<\/span><\/span><span class=\"base\"><span class=\"mord\">8<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">56<\/span><\/span><\/span><\/span>, add <strong data-start=\"756\" data-end=\"762\">25<\/strong> \u2192 <strong data-start=\"765\" data-end=\"773\">5625<\/strong><\/li>\n<\/ul>\n<p data-start=\"777\" data-end=\"810\"><strong data-start=\"779\" data-end=\"790\">Answer:<\/strong> <span class=\"katex\"><span class=\"katex-mathml\">752=562575^2 = 5625<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">7<\/span><span class=\"mord\">5<span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">5625<\/span><\/span><\/span><\/span><\/p>\n<h3 data-start=\"817\" data-end=\"856\"><strong data-start=\"821\" data-end=\"854\">\u00a0Square of Numbers Near 50<\/strong><\/h3>\n<p data-start=\"857\" data-end=\"909\">For numbers close to <strong data-start=\"878\" data-end=\"884\">50<\/strong> (<span class=\"katex\"><span class=\"katex-mathml\">50\u00b1x50 \\pm x<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">50<\/span><span class=\"mbin\">\u00b1<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span>), use:<\/p>\n<p data-start=\"911\" data-end=\"928\"><strong data-start=\"914\" data-end=\"926\">Formula:<\/strong><\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">N2=25+x\u2223x2N^2 = 25 + x \\quad | \\quad x^2<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">N<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">25<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><span class=\"mord\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p data-start=\"967\" data-end=\"995\"><strong data-start=\"970\" data-end=\"982\">Example:<\/strong> <span class=\"katex\"><span class=\"katex-mathml\">48248^2<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">4<\/span><span class=\"mord\">8<span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<ul data-start=\"996\" data-end=\"1085\">\n<li data-start=\"996\" data-end=\"1021\"><span class=\"katex\"><span class=\"katex-mathml\">x=50\u221248=2x = 50 &#8211; 48 = 2<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">50<\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">48<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/li>\n<li data-start=\"1022\" data-end=\"1060\"><span class=\"katex\"><span class=\"katex-mathml\">25\u22122=2325 &#8211; 2 = 23<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">25<\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">2<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">23<\/span><\/span><\/span><\/span> | <span class=\"katex\"><span class=\"katex-mathml\">22=042^2 = 04<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">2<span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">04<\/span><\/span><\/span><\/span><\/li>\n<li data-start=\"1061\" data-end=\"1085\"><strong data-start=\"1063\" data-end=\"1074\">Answer:<\/strong> <strong data-start=\"1075\" data-end=\"1083\">2304<\/strong><\/li>\n<\/ul>\n<p data-start=\"1087\" data-end=\"1115\"><strong data-start=\"1090\" data-end=\"1102\">Example:<\/strong> <span class=\"katex\"><span class=\"katex-mathml\">52252^2<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">5<\/span><span class=\"mord\">2<span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<ul data-start=\"1116\" data-end=\"1205\">\n<li data-start=\"1116\" data-end=\"1141\"><span class=\"katex\"><span class=\"katex-mathml\">x=52\u221250=2x = 52 &#8211; 50 = 2<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">52<\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">50<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/li>\n<li data-start=\"1142\" data-end=\"1180\"><span class=\"katex\"><span class=\"katex-mathml\">25+2=2725 + 2 = 27<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">25<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">2<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">27<\/span><\/span><\/span><\/span> | <span class=\"katex\"><span class=\"katex-mathml\">22=042^2 = 04<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">2<span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">04<\/span><\/span><\/span><\/span><\/li>\n<li data-start=\"1181\" data-end=\"1205\"><strong data-start=\"1183\" data-end=\"1194\">Answer:<\/strong> <strong data-start=\"1195\" data-end=\"1203\">2704<\/strong><\/li>\n<\/ul>\n<h3 data-start=\"1212\" data-end=\"1256\"><strong data-start=\"1216\" data-end=\"1254\">\u00a0Square of Numbers Close to 100<\/strong><\/h3>\n<p data-start=\"1257\" data-end=\"1311\">For numbers close to <strong data-start=\"1278\" data-end=\"1285\">100<\/strong> (<span class=\"katex\"><span class=\"katex-mathml\">100\u00b1x100 \\pm x<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">100<\/span><span class=\"mbin\">\u00b1<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span>), use:<\/p>\n<p data-start=\"1313\" data-end=\"1330\"><strong data-start=\"1316\" data-end=\"1328\">Formula:<\/strong><\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">N2=(100+x)\u00d7(100+x)=(100+2x)\u2223x2N^2 = (100 + x) \\times (100 + x) = (100 + 2x) | x^2<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">N<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord\">100<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mbin\">\u00d7<\/span><\/span><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord\">100<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord\">100<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">2<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mord\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p data-start=\"1390\" data-end=\"1418\"><strong data-start=\"1393\" data-end=\"1405\">Example:<\/strong> <span class=\"katex\"><span class=\"katex-mathml\">96296^2<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">9<\/span><span class=\"mord\">6<span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<ul data-start=\"1419\" data-end=\"1520\">\n<li data-start=\"1419\" data-end=\"1445\"><span class=\"katex\"><span class=\"katex-mathml\">100\u221296=4100 &#8211; 96 = 4<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">100<\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">96<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">4<\/span><\/span><\/span><\/span>, so<\/li>\n<li data-start=\"1446\" data-end=\"1495\"><span class=\"katex\"><span class=\"katex-mathml\">(96+4)=96+4=92(96 + 4) = 96 + 4 = 92<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord\">96<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">4<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">96<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">4<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">92<\/span><\/span><\/span><\/span> | <span class=\"katex\"><span class=\"katex-mathml\">42=164^2 = 16<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">4<span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">16<\/span><\/span><\/span><\/span><\/li>\n<li data-start=\"1496\" data-end=\"1520\"><strong data-start=\"1498\" data-end=\"1509\">Answer:<\/strong> <strong data-start=\"1510\" data-end=\"1518\">9216<\/strong><\/li>\n<\/ul>\n<p data-start=\"1522\" data-end=\"1551\"><strong data-start=\"1525\" data-end=\"1537\">Example:<\/strong> <span class=\"katex\"><span class=\"katex-mathml\">1042104^2<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">10<\/span><span class=\"mord\">4<span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<ul data-start=\"1552\" data-end=\"1618\">\n<li data-start=\"1552\" data-end=\"1592\"><span class=\"katex\"><span class=\"katex-mathml\">104+4=108104 + 4 = 108<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">104<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">4<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">108<\/span><\/span><\/span><\/span> | <span class=\"katex\"><span class=\"katex-mathml\">42=164^2 = 16<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">4<span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">16<\/span><\/span><\/span><\/span><\/li>\n<li data-start=\"1593\" data-end=\"1618\"><strong data-start=\"1595\" data-end=\"1606\">Answer:<\/strong> <strong data-start=\"1607\" data-end=\"1616\">10816<\/strong><\/li>\n<\/ul>\n<h3 data-start=\"1625\" data-end=\"1692\"><strong data-start=\"1628\" data-end=\"1690\">\u00a0Square Root Tricks (\u0924\u0947\u091c\u0940 \u0938\u0947 \u0935\u0930\u094d\u0917\u092e\u0942\u0932 \u0928\u093f\u0915\u093e\u0932\u0928\u0947 \u0915\u0940 \u091f\u094d\u0930\u093f\u0915\u094d\u0938)<\/strong><\/h3>\n<h3 data-start=\"1694\" data-end=\"1738\"><strong data-start=\"1698\" data-end=\"1736\">\u00a0Perfect Squares Identification<\/strong><\/h3>\n<p data-start=\"1739\" data-end=\"1811\">If a number ends in <strong data-start=\"1759\" data-end=\"1773\">2, 3, 7, 8<\/strong>, it <strong data-start=\"1778\" data-end=\"1788\">cannot<\/strong> be a perfect square.<\/p>\n<p data-start=\"1813\" data-end=\"1881\"><strong data-start=\"1816\" data-end=\"1828\">Example:<\/strong> <span class=\"katex\"><span class=\"katex-mathml\">743743<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">743<\/span><\/span><\/span><\/span> \u2192 Ends in 3 \u2192\u00a0 <strong data-start=\"1855\" data-end=\"1879\">Not a perfect square<\/strong><\/p>\n<p data-start=\"1883\" data-end=\"1958\"><strong data-start=\"1886\" data-end=\"1898\">Example:<\/strong> <span class=\"katex\"><span class=\"katex-mathml\">441441<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">441<\/span><\/span><\/span><\/span> \u2192 Ends in 1 \u2192\u00a0 <strong data-start=\"1925\" data-end=\"1956\">Perfect square (<span class=\"katex\"><span class=\"katex-mathml\">21221^2<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">2<\/span><span class=\"mord\">1<span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/strong><\/p>\n<h3 data-start=\"1965\" data-end=\"2023\"><strong data-start=\"1969\" data-end=\"2021\">\u00a0Square Root of Perfect Squares (Quick Trick)<\/strong><\/h3>\n<p data-start=\"2024\" data-end=\"2120\">For perfect squares, break the number into <strong data-start=\"2067\" data-end=\"2080\">two parts<\/strong> and identify the nearest square root.<\/p>\n<p data-start=\"2122\" data-end=\"2157\"><strong data-start=\"2125\" data-end=\"2137\">Example:<\/strong> <span class=\"katex\"><span class=\"katex-mathml\">4489\\sqrt{4489}<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"svg-align\"><span class=\"mord\">4489<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<ul data-start=\"2158\" data-end=\"2327\">\n<li data-start=\"2158\" data-end=\"2241\">First two digits \u2192 <strong data-start=\"2179\" data-end=\"2185\">44<\/strong> (Nearest square = <strong data-start=\"2204\" data-end=\"2220\">6<span class=\"katex\"><span class=\"katex-mathml\">2^2<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> = 36<\/strong>, <strong data-start=\"2222\" data-end=\"2238\">7<span class=\"katex\"><span class=\"katex-mathml\">2^2<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> = 49<\/strong>)<\/li>\n<li data-start=\"2242\" data-end=\"2298\">Last digit \u2192 <strong data-start=\"2257\" data-end=\"2262\">9<\/strong> (So the unit place is <strong data-start=\"2285\" data-end=\"2295\">3 or 7<\/strong>)<\/li>\n<li data-start=\"2299\" data-end=\"2327\">Check: <span class=\"katex\"><span class=\"katex-mathml\">672=448967^2 = 4489<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">6<\/span><span class=\"mord\">7<span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">4489<\/span><\/span><\/span><\/span><\/li>\n<\/ul>\n<p data-start=\"2329\" data-end=\"2351\"><strong data-start=\"2331\" data-end=\"2342\">Answer:<\/strong> <strong data-start=\"2343\" data-end=\"2349\">67<\/strong><\/p>\n<h3 data-start=\"2358\" data-end=\"2418\"><strong data-start=\"2362\" data-end=\"2416\">\u00a0Estimating Square Roots of Non-Perfect Squares<\/strong><\/h3>\n<p data-start=\"2419\" data-end=\"2484\">Find the <strong data-start=\"2428\" data-end=\"2455\">nearest perfect squares<\/strong> and <strong data-start=\"2460\" data-end=\"2481\">use approximation<\/strong>.<\/p>\n<p data-start=\"2486\" data-end=\"2519\"><strong data-start=\"2489\" data-end=\"2501\">Example:<\/strong> <span class=\"katex\"><span class=\"katex-mathml\">50\\sqrt{50}<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"svg-align\"><span class=\"mord\">50<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<ul data-start=\"2520\" data-end=\"2623\">\n<li data-start=\"2520\" data-end=\"2578\">Nearest squares: <strong data-start=\"2539\" data-end=\"2576\"><span class=\"katex\"><span class=\"katex-mathml\">49(72)49 (7^2)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">49<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">7<span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span> and <span class=\"katex\"><span class=\"katex-mathml\">64(82)64 (8^2)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">64<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">8<span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/strong><\/li>\n<li data-start=\"2579\" data-end=\"2623\">Since 50 is closer to 49, <strong data-start=\"2607\" data-end=\"2621\">\u221a50 \u2248 7.07<\/strong><\/li>\n<\/ul>\n<h3 data-start=\"2630\" data-end=\"2674\"><strong data-start=\"2634\" data-end=\"2672\">\u00a0Final Tips for Quick Calculation<\/strong><\/h3>\n<p data-start=\"2675\" data-end=\"2827\">\u00a0Memorize squares of <strong data-start=\"2697\" data-end=\"2708\">1 to 30<\/strong><br data-start=\"2708\" data-end=\"2711\" \/>\u00a0Use <strong data-start=\"2717\" data-end=\"2741\">approximation tricks<\/strong> for non-perfect squares<br data-start=\"2765\" data-end=\"2768\" \/>\u00a0Practice <strong data-start=\"2779\" data-end=\"2799\">breaking numbers<\/strong> into smaller calculations<\/p>\n<p data-start=\"2829\" data-end=\"2904\" data-is-last-node=\"\" data-is-only-node=\"\">With these tricks, <strong data-start=\"2848\" data-end=\"2901\">you\u2019ll solve squares and square roots in seconds!<\/strong><\/p>\n<h3 data-start=\"2829\" data-end=\"2904\"><a href=\"https:\/\/teachmint.storage.googleapis.com\/public\/817166298\/StudyMaterial\/6078dc9b-178d-4abf-888b-aa78669af45c.pdf\" target=\"_blank\" rel=\"noopener\">Mathematics Short Tricks\/SQUARE TRICKS AND SQUARE ROOT TRICKS IN MATHEMATICS.<\/a><\/h3>\n<h3 class=\"LC20lb MBeuO DKV0Md\"><a href=\"https:\/\/mathlearners.com\/wp-content\/gallery\/files\/vedic%20mathematics.pdf\" target=\"_blank\" rel=\"noopener\">Vedic Mathematics Tricks and Shortcuts<\/a><\/h3>\n<h3 class=\"LC20lb MBeuO DKV0Md\"><a href=\"https:\/\/ijmsi.org\/Papers\/Volume.2.Issue.9\/F029024031.pdf\" target=\"_blank\" rel=\"noopener\">Squares and Square Roots<\/a><\/h3>\n<p data-start=\"0\" data-end=\"200\">Here are some super helpful and easy-to-remember <strong data-start=\"49\" data-end=\"77\">Mathematics Short Tricks<\/strong> for <strong data-start=\"82\" data-end=\"92\">Square<\/strong> and <strong data-start=\"97\" data-end=\"125\">Square Root Calculations<\/strong>, perfect for competitive exams like SSC, Railways, Banking, and even GATE.<\/p>\n<hr data-start=\"202\" data-end=\"205\" \/>\n<h2 data-start=\"207\" data-end=\"253\">\ud83d\udcd0 <strong data-start=\"213\" data-end=\"253\">SQUARE TRICKS (\u0935\u0930\u094d\u0917 \u0915\u0930\u0928\u0947 \u0915\u0940 \u091f\u094d\u0930\u093f\u0915\u094d\u0938)<\/strong><\/h2>\n<h3 data-start=\"255\" data-end=\"297\">\u2705 <strong data-start=\"261\" data-end=\"297\">1. Square of numbers ending in 5<\/strong><\/h3>\n<p data-start=\"298\" data-end=\"402\"><strong data-start=\"298\" data-end=\"308\">Trick:<\/strong><br data-start=\"308\" data-end=\"311\" \/>If a number ends in 5, like 25, 35, 75 etc.<br data-start=\"354\" data-end=\"357\" \/>Use the formula:<br data-start=\"373\" data-end=\"376\" \/><strong data-start=\"376\" data-end=\"402\">(a5)\u00b2 = a \u00d7 (a+1) | 25<\/strong><\/p>\n<p data-start=\"404\" data-end=\"420\">\ud83d\udccc <strong data-start=\"407\" data-end=\"420\">Examples:<\/strong><\/p>\n<ul data-start=\"421\" data-end=\"513\">\n<li data-start=\"421\" data-end=\"450\">\n<p data-start=\"423\" data-end=\"450\">25\u00b2 = 2 \u00d7 3 = 6 \u21d2 <strong data-start=\"441\" data-end=\"448\">625<\/strong><\/p>\n<\/li>\n<li data-start=\"451\" data-end=\"482\">\n<p data-start=\"453\" data-end=\"482\">85\u00b2 = 8 \u00d7 9 = 72 \u21d2 <strong data-start=\"472\" data-end=\"480\">7225<\/strong><\/p>\n<\/li>\n<li data-start=\"483\" data-end=\"513\">\n<p data-start=\"485\" data-end=\"513\">95\u00b2 = 9 \u00d7 10 = 90 \u21d2 <strong data-start=\"505\" data-end=\"513\">9025<\/strong><\/p>\n<\/li>\n<\/ul>\n<hr data-start=\"515\" data-end=\"518\" \/>\n<h3 data-start=\"520\" data-end=\"559\">\u2705 <strong data-start=\"526\" data-end=\"559\">2. Square of numbers near 100<\/strong><\/h3>\n<p data-start=\"560\" data-end=\"691\"><strong data-start=\"560\" data-end=\"570\">Trick:<\/strong><br data-start=\"570\" data-end=\"573\" \/>Let the number be <strong data-start=\"591\" data-end=\"604\">(100 \u00b1 x)<\/strong><br data-start=\"604\" data-end=\"607\" \/>Use:<br data-start=\"611\" data-end=\"614\" \/><strong data-start=\"614\" data-end=\"651\">(100 + x)\u00b2 = 10000 + 2\u00d7100\u00d7x + x\u00b2<\/strong><br data-start=\"651\" data-end=\"654\" \/><strong data-start=\"654\" data-end=\"691\">(100 &#8211; x)\u00b2 = 10000 &#8211; 2\u00d7100\u00d7x + x\u00b2<\/strong><\/p>\n<p data-start=\"693\" data-end=\"709\">\ud83d\udccc <strong data-start=\"696\" data-end=\"709\">Examples:<\/strong><\/p>\n<ul data-start=\"710\" data-end=\"791\">\n<li data-start=\"710\" data-end=\"752\">\n<p data-start=\"712\" data-end=\"752\">102\u00b2 = 10000 + 2\u00d7100\u00d72 + 4 = <strong data-start=\"741\" data-end=\"750\">10404<\/strong><\/p>\n<\/li>\n<li data-start=\"753\" data-end=\"791\">\n<p data-start=\"755\" data-end=\"791\">98\u00b2 = 10000 &#8211; 2\u00d7100\u00d72 + 4 = <strong data-start=\"783\" data-end=\"791\">9604<\/strong><\/p>\n<\/li>\n<\/ul>\n<hr data-start=\"793\" data-end=\"796\" \/>\n<h3 data-start=\"798\" data-end=\"844\">\u2705 <strong data-start=\"804\" data-end=\"844\">3. Square of 2-digit numbers quickly<\/strong><\/h3>\n<p data-start=\"845\" data-end=\"893\">Use the identity:<br data-start=\"862\" data-end=\"865\" \/><strong data-start=\"865\" data-end=\"893\">(a + b)\u00b2 = a\u00b2 + 2ab + b\u00b2<\/strong><\/p>\n<p data-start=\"895\" data-end=\"906\">\ud83d\udccc Example:<\/p>\n<ul data-start=\"907\" data-end=\"956\">\n<li data-start=\"907\" data-end=\"956\">\n<p data-start=\"909\" data-end=\"956\">47\u00b2 = (40 + 7)\u00b2 = 1600 + 2\u00d740\u00d77 + 49 = <strong data-start=\"948\" data-end=\"956\">2209<\/strong><\/p>\n<\/li>\n<\/ul>\n<hr data-start=\"958\" data-end=\"961\" \/>\n<h3 data-start=\"963\" data-end=\"1002\">\u2705 <strong data-start=\"969\" data-end=\"1002\">4. Square between two numbers<\/strong><\/h3>\n<p data-start=\"1003\" data-end=\"1015\">If you know:<\/p>\n<ul data-start=\"1016\" data-end=\"1135\">\n<li data-start=\"1016\" data-end=\"1029\">\n<p data-start=\"1018\" data-end=\"1029\">30\u00b2 = 900<\/p>\n<\/li>\n<li data-start=\"1030\" data-end=\"1135\">\n<p data-start=\"1032\" data-end=\"1135\">31\u00b2 = 961<br data-start=\"1041\" data-end=\"1044\" \/>then estimate:<br data-start=\"1058\" data-end=\"1061\" \/><strong data-start=\"1061\" data-end=\"1135\">30.5\u00b2 = (30 + 0.5)\u00b2 = 30\u00b2 + 2\u00d730\u00d70.5 + 0.25 = 900 + 30 + 0.25 = 930.25<\/strong><\/p>\n<\/li>\n<\/ul>\n<hr data-start=\"1137\" data-end=\"1140\" \/>\n<h2 data-start=\"1142\" data-end=\"1199\">\ud83d\udccf <strong data-start=\"1148\" data-end=\"1199\">SQUARE ROOT TRICKS (\u0935\u0930\u094d\u0917\u092e\u0942\u0932 \u0928\u093f\u0915\u093e\u0932\u0928\u0947 \u0915\u0940 \u091f\u094d\u0930\u093f\u0915\u094d\u0938)<\/strong><\/h2>\n<h3 data-start=\"1201\" data-end=\"1258\">\u2705 <strong data-start=\"1207\" data-end=\"1258\">1. Square roots of perfect squares (up to 1000)<\/strong><\/h3>\n<ul data-start=\"1259\" data-end=\"1408\">\n<li data-start=\"1259\" data-end=\"1295\">\n<p data-start=\"1261\" data-end=\"1295\">Memorize squares of numbers 1\u201330<\/p>\n<\/li>\n<li data-start=\"1296\" data-end=\"1408\">\n<p data-start=\"1298\" data-end=\"1319\">Reverse lookup trick:<\/p>\n<ul data-start=\"1322\" data-end=\"1408\">\n<li data-start=\"1322\" data-end=\"1361\">\n<p data-start=\"1324\" data-end=\"1361\">If number ends in 25 \u2192 root ends in 5<\/p>\n<\/li>\n<li data-start=\"1364\" data-end=\"1408\">\n<p data-start=\"1366\" data-end=\"1408\">If number ends in 76 \u2192 root ends in 4 or 6<\/p>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p data-start=\"1410\" data-end=\"1421\">\ud83d\udccc Example:<\/p>\n<ul data-start=\"1422\" data-end=\"1456\">\n<li data-start=\"1422\" data-end=\"1439\">\n<p data-start=\"1424\" data-end=\"1439\">\u221a625 = <strong data-start=\"1431\" data-end=\"1437\">25<\/strong><\/p>\n<\/li>\n<li data-start=\"1440\" data-end=\"1456\">\n<p data-start=\"1442\" data-end=\"1456\">\u221a1225 = <strong data-start=\"1450\" data-end=\"1456\">35<\/strong><\/p>\n<\/li>\n<\/ul>\n<hr data-start=\"1458\" data-end=\"1461\" \/>\n<h3 data-start=\"1463\" data-end=\"1520\">\u2705 <strong data-start=\"1469\" data-end=\"1520\">2. Square Root Estimation (Non-perfect squares)<\/strong><\/h3>\n<p data-start=\"1522\" data-end=\"1525\">If:<\/p>\n<ul data-start=\"1526\" data-end=\"1642\">\n<li data-start=\"1526\" data-end=\"1564\">\n<p data-start=\"1528\" data-end=\"1564\">\u221a50 is between \u221a49 = 7 and \u221a64 = 8<\/p>\n<\/li>\n<li data-start=\"1565\" data-end=\"1642\">\n<p data-start=\"1567\" data-end=\"1642\">Use linear approximation:<br \/>\n\u221a50 \u2248 7 + (50 \u2013 49)\/[2\u00d77] = 7 + 1\/14 \u2248 <strong data-start=\"1634\" data-end=\"1642\">7.07<\/strong><\/p>\n<\/li>\n<\/ul>\n<hr data-start=\"1644\" data-end=\"1647\" \/>\n<h3 data-start=\"1649\" data-end=\"1690\">\u2705 <strong data-start=\"1655\" data-end=\"1690\">3. Shortcut Table: Squares 1\u201330<\/strong><\/h3>\n<div class=\"_tableContainer_16hzy_1\">\n<div class=\"_tableWrapper_16hzy_14 group flex w-fit flex-col-reverse\">\n<table class=\"w-fit min-w-(--thread-content-width)\" data-start=\"1692\" data-end=\"1850\">\n<thead data-start=\"1692\" data-end=\"1710\">\n<tr data-start=\"1692\" data-end=\"1710\">\n<th data-start=\"1692\" data-end=\"1697\" data-col-size=\"sm\">n<\/th>\n<th data-start=\"1697\" data-end=\"1703\" data-col-size=\"sm\">n\u00b2<\/th>\n<th data-start=\"1703\" data-end=\"1710\" data-col-size=\"sm\">\u221an\u00b2<\/th>\n<\/tr>\n<\/thead>\n<tbody data-start=\"1731\" data-end=\"1850\">\n<tr data-start=\"1731\" data-end=\"1750\">\n<td data-start=\"1731\" data-end=\"1736\" data-col-size=\"sm\">5<\/td>\n<td data-start=\"1736\" data-end=\"1742\" data-col-size=\"sm\">25<\/td>\n<td data-start=\"1742\" data-end=\"1750\" data-col-size=\"sm\">5<\/td>\n<\/tr>\n<tr data-start=\"1751\" data-end=\"1770\">\n<td data-start=\"1751\" data-end=\"1756\" data-col-size=\"sm\">10<\/td>\n<td data-start=\"1756\" data-end=\"1762\" data-col-size=\"sm\">100<\/td>\n<td data-start=\"1762\" data-end=\"1770\" data-col-size=\"sm\">10<\/td>\n<\/tr>\n<tr data-start=\"1771\" data-end=\"1790\">\n<td data-start=\"1771\" data-end=\"1776\" data-col-size=\"sm\">15<\/td>\n<td data-start=\"1776\" data-end=\"1782\" data-col-size=\"sm\">225<\/td>\n<td data-start=\"1782\" data-end=\"1790\" data-col-size=\"sm\">15<\/td>\n<\/tr>\n<tr data-start=\"1791\" data-end=\"1810\">\n<td data-start=\"1791\" data-end=\"1796\" data-col-size=\"sm\">20<\/td>\n<td data-start=\"1796\" data-end=\"1802\" data-col-size=\"sm\">400<\/td>\n<td data-start=\"1802\" data-end=\"1810\" data-col-size=\"sm\">20<\/td>\n<\/tr>\n<tr data-start=\"1811\" data-end=\"1830\">\n<td data-start=\"1811\" data-end=\"1816\" data-col-size=\"sm\">25<\/td>\n<td data-start=\"1816\" data-end=\"1822\" data-col-size=\"sm\">625<\/td>\n<td data-start=\"1822\" data-end=\"1830\" data-col-size=\"sm\">25<\/td>\n<\/tr>\n<tr data-start=\"1831\" data-end=\"1850\">\n<td data-start=\"1831\" data-end=\"1836\" data-col-size=\"sm\">30<\/td>\n<td data-start=\"1836\" data-end=\"1842\" data-col-size=\"sm\">900<\/td>\n<td data-start=\"1842\" data-end=\"1850\" data-col-size=\"sm\">30<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"sticky end-(--thread-content-margin) h-0 self-end select-none\">\n<div class=\"absolute end-0 flex items-end\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<hr data-start=\"1852\" data-end=\"1855\" \/>\n<h2 data-start=\"1857\" data-end=\"1873\">\ud83d\udd25 Bonus Tip:<\/h2>\n<h3 data-start=\"1874\" data-end=\"1914\">\ud83d\udd04 <strong data-start=\"1881\" data-end=\"1914\">Digit Root Check for Squares:<\/strong><\/h3>\n<p data-start=\"1915\" data-end=\"1991\">Only numbers whose <strong data-start=\"1934\" data-end=\"1967\">digital root is 1, 4, 7, or 9<\/strong> can be perfect squares.<\/p>\n<p data-start=\"1993\" data-end=\"2045\">Example:<br data-start=\"2001\" data-end=\"2004\" \/>121 \u2192 1+2+1 = 4 \u2192 \u2705<br data-start=\"2023\" data-end=\"2026\" \/>123 \u2192 1+2+3 = 6 \u2192 \u274c<\/p>\n<hr data-start=\"2047\" data-end=\"2050\" \/>\n<h2 data-start=\"2052\" data-end=\"2085\">\ud83e\udde0 Want a PDF or Video Format?<\/h2>\n<p data-start=\"2086\" data-end=\"2097\">I can make:<\/p>\n<ul data-start=\"2098\" data-end=\"2209\">\n<li data-start=\"2098\" data-end=\"2131\">\n<p data-start=\"2100\" data-end=\"2131\"><strong data-start=\"2100\" data-end=\"2131\">Handwritten-style PDF notes<\/strong><\/p>\n<\/li>\n<li data-start=\"2132\" data-end=\"2174\">\n<p data-start=\"2134\" data-end=\"2174\"><strong data-start=\"2134\" data-end=\"2174\">Video Script for Teaching or YouTube<\/strong><\/p>\n<\/li>\n<li data-start=\"2175\" data-end=\"2209\">\n<p data-start=\"2177\" data-end=\"2209\"><strong data-start=\"2177\" data-end=\"2209\">Practice Questions &amp; Quizzes<\/strong><\/p>\n<\/li>\n<\/ul>\n<p data-start=\"2211\" data-end=\"2239\" data-is-last-node=\"\" data-is-only-node=\"\">Would you like one of these?<\/p>\n<h3 data-start=\"2211\" data-end=\"2239\"><a href=\"https:\/\/www.jaipuria.ac.in\/blog\/wp-content\/uploads\/2023\/07\/Quant-Short-Tricks-PDF.pdf\" target=\"_blank\" rel=\"noopener\">Mathematics Short Tricks\/SQUARE TRICKS AND SQUARE ROOT TRICKS IN MATHEMATICS.<\/a><\/h3>\n","protected":false},"excerpt":{"rendered":"<p>Mathematics Short Tricks\/SQUARE TRICKS AND SQUARE ROOT TRICKS IN MATHEMATICS. [fvplayer id=&#8221;671&#8243;] Mathematics Short Tricks \u2013 Square &amp; Square Root Tricks Learning square and square root tricks helps in fast calculations, which is useful for competitive exams like SSC, Banking, GATE, and more. Below are some powerful tricks to speed up your calculations. \u00a0Square Tricks [&hellip;]<\/p>\n","protected":false},"author":64,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[83],"tags":[],"class_list":["post-4234","post","type-post","status-publish","format-standard","hentry","category-mathematics-short-tricks"],"_links":{"self":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/4234","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/users\/64"}],"replies":[{"embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/comments?post=4234"}],"version-history":[{"count":0,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/4234\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/media?parent=4234"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/categories?post=4234"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/tags?post=4234"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}