{"id":4199,"date":"2025-06-06T14:47:18","date_gmt":"2025-06-06T14:47:18","guid":{"rendered":"https:\/\/diznr.com\/?p=4199"},"modified":"2025-06-06T14:47:18","modified_gmt":"2025-06-06T14:47:18","slug":"mathematics-short-tricks-square-root-tricks-for-tricks-placement","status":"publish","type":"post","link":"https:\/\/www.reilsolar.com\/pdf\/mathematics-short-tricks-square-root-tricks-for-tricks-placement\/","title":{"rendered":"Mathematics Short Tricks\/ SQUARE ROOT Tricks for Placement tricks."},"content":{"rendered":"<p>Mathematics Short Tricks\/ SQUARE ROOT Tricks for Placement tricks.<\/p>\n<p>[fvplayer id=&#8221;654&#8243;]<\/p>\n<h3 data-start=\"0\" data-end=\"80\"><strong data-start=\"7\" data-end=\"73\">Square Root Tricks for Quick Calculation &#8211; Placement Exam Tips<\/strong><\/h3>\n<h3 data-start=\"87\" data-end=\"121\"><strong data-start=\"90\" data-end=\"119\">\u00a0What is a Square Root?<\/strong><\/h3>\n<p data-start=\"122\" data-end=\"251\">The square root of a number <strong data-start=\"150\" data-end=\"155\">x<\/strong> is a number <strong data-start=\"168\" data-end=\"173\">y<\/strong> such that <span class=\"katex\"><span class=\"katex-mathml\">y2=xy^2 = x<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">y<\/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 mathnormal\">x<\/span><\/span><\/span><\/span>.<br data-start=\"198\" data-end=\"201\" \/>Example:<br data-start=\"209\" data-end=\"212\" \/><span class=\"katex\"><span class=\"katex-mathml\">25=5\\sqrt{25} = 5<\/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\">25<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">5<\/span><\/span><\/span><\/span> because <span class=\"katex\"><span class=\"katex-mathml\">52=255^2 = 25<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><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\">25<\/span><\/span><\/span><\/span>.<\/p>\n<h3 data-start=\"258\" data-end=\"317\"><strong data-start=\"264\" data-end=\"315\">Square Root Short Tricks for Quick Calculation:<\/strong><\/h3>\n<h3 data-start=\"319\" data-end=\"354\"><strong data-start=\"323\" data-end=\"352\">1. Perfect Square Method:<\/strong><\/h3>\n<p data-start=\"355\" data-end=\"424\">If the number is a <strong data-start=\"374\" data-end=\"392\">perfect square<\/strong>, simply find its square root.<\/p>\n<ul data-start=\"425\" data-end=\"486\">\n<li data-start=\"425\" data-end=\"457\">Example: <span class=\"katex\"><span class=\"katex-mathml\">144=12\\sqrt{144} = 12<\/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\">144<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">12<\/span><\/span><\/span><\/span><\/li>\n<li data-start=\"458\" data-end=\"486\">Example: <span class=\"katex\"><span class=\"katex-mathml\">81=9\\sqrt{81} = 9<\/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\">81<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">9<\/span><\/span><\/span><\/span><\/li>\n<\/ul>\n<h3 data-start=\"493\" data-end=\"548\"><strong data-start=\"497\" data-end=\"546\">2. Estimation Method for Non-Perfect Squares:<\/strong><\/h3>\n<p data-start=\"549\" data-end=\"610\">Estimate between which two perfect squares the number lies.<\/p>\n<ul data-start=\"611\" data-end=\"711\">\n<li data-start=\"611\" data-end=\"711\">Example: <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> lies between <span class=\"katex\"><span class=\"katex-mathml\">72=497^2 = 49<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><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\">49<\/span><\/span><\/span><\/span> and <span class=\"katex\"><span class=\"katex-mathml\">82=648^2 = 64<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><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=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">64<\/span><\/span><\/span><\/span>.<br data-start=\"679\" data-end=\"682\" \/>Approximate value: 7.1 or 7.2<\/li>\n<\/ul>\n<h3 data-start=\"718\" data-end=\"763\"><strong data-start=\"722\" data-end=\"761\">3. Division Method (Long Division):<\/strong><\/h3>\n<p data-start=\"764\" data-end=\"825\">Used for precise square root calculation for large numbers.<\/p>\n<ul data-start=\"826\" data-end=\"1022\">\n<li data-start=\"826\" data-end=\"1022\">Example: <span class=\"katex\"><span class=\"katex-mathml\">324\\sqrt{324}<\/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\">324<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><br data-start=\"851\" data-end=\"854\" \/>Divide the number into pairs from right to left: <strong data-start=\"903\" data-end=\"913\">3 | 24<\/strong><br data-start=\"913\" data-end=\"916\" \/>Try <span class=\"katex\"><span class=\"katex-mathml\">11<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">1<\/span><\/span><\/span><\/span> (1 \u00d7 1 = 1) \u2192 Subtract (3 &#8211; 1 = 2) \u2192 Bring down <strong data-start=\"974\" data-end=\"980\">24<\/strong> \u2192 Try <strong data-start=\"987\" data-end=\"992\">8<\/strong> (28 \u00d7 8 = 224)<br data-start=\"1007\" data-end=\"1010\" \/>Answer: 18<\/li>\n<\/ul>\n<h3 data-start=\"1029\" data-end=\"1068\"><strong data-start=\"1033\" data-end=\"1066\">4. Using Unit Digit Analysis:<\/strong><\/h3>\n<p data-start=\"1069\" data-end=\"1149\">Perfect squares end in <strong data-start=\"1092\" data-end=\"1112\">0, 1, 4, 5, 6, 9<\/strong>. Use this to find the square root.<\/p>\n<ul data-start=\"1150\" data-end=\"1264\">\n<li data-start=\"1150\" data-end=\"1264\">Example: Find <span class=\"katex\"><span class=\"katex-mathml\">784\\sqrt{784}<\/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\">784<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><br data-start=\"1180\" data-end=\"1183\" \/>Last digit <strong data-start=\"1194\" data-end=\"1199\">4<\/strong> means root ends in <strong data-start=\"1219\" data-end=\"1229\">2 or 8<\/strong>.<br data-start=\"1230\" data-end=\"1233\" \/><span class=\"katex\"><span class=\"katex-mathml\">282=78428^2 = 784<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">2<\/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=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">784<\/span><\/span><\/span><\/span> \u21d2 Answer: <strong data-start=\"1258\" data-end=\"1264\">28<\/strong><\/li>\n<\/ul>\n<h3 data-start=\"1271\" data-end=\"1322\"><strong data-start=\"1275\" data-end=\"1320\">5. Quick Trick for Numbers between 40-60:<\/strong><\/h3>\n<p data-start=\"1323\" data-end=\"1467\">Use the formula:<br data-start=\"1339\" data-end=\"1342\" \/><span class=\"katex\"><span class=\"katex-mathml\">(a2+b)\u2248a+b2a\\sqrt{(a^2 + b)} \\approx a + \\frac{b}{2a}<\/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\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"mbin\">+<\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><span class=\"mrel\">\u2248<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">a<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<span class=\"mord mathnormal mtight\">a<\/span><\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">b<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><br data-start=\"1387\" data-end=\"1390\" \/>where <span class=\"katex\"><span class=\"katex-mathml\">aa<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">a<\/span><\/span><\/span><\/span> is the nearest perfect square root and <span class=\"katex\"><span class=\"katex-mathml\">bb<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">b<\/span><\/span><\/span><\/span> is the difference.<\/p>\n<ul data-start=\"1468\" data-end=\"1604\">\n<li data-start=\"1468\" data-end=\"1604\">Example: <span class=\"katex\"><span class=\"katex-mathml\">47\\sqrt{47}<\/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\">47<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><br data-start=\"1492\" data-end=\"1495\" \/>Nearest perfect square = 49 (7\u00b2)<br data-start=\"1527\" data-end=\"1530\" \/><span class=\"katex\"><span class=\"katex-mathml\">49\u221247=249 &#8211; 47 = 2<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">49<\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">47<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">2<\/span><\/span><\/span><\/span><br data-start=\"1545\" data-end=\"1548\" \/><span class=\"katex\"><span class=\"katex-mathml\">47\u22487\u2212214=7\u22120.14=6.86\\sqrt{47} \\approx 7 &#8211; \\frac{2}{14} = 7 &#8211; 0.14 = 6.86<\/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\">47<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><span class=\"mrel\">\u2248<\/span><\/span><span class=\"base\"><span class=\"mord\">7<\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">14<\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">7<\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">0.14<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">6.86<\/span><\/span><\/span><\/span><\/li>\n<\/ul>\n<h3 data-start=\"1611\" data-end=\"1658\"><strong data-start=\"1615\" data-end=\"1656\">6. Shortcut for Decimal Square Roots:<\/strong><\/h3>\n<p data-start=\"1659\" data-end=\"1732\">To find the square root of decimals, make pairs from the decimal point.<\/p>\n<ul data-start=\"1733\" data-end=\"1890\">\n<li data-start=\"1733\" data-end=\"1890\">Example: <span class=\"katex\"><span class=\"katex-mathml\">0.0049\\sqrt{0.0049}<\/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\">0.0049<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><br data-start=\"1761\" data-end=\"1764\" \/>Pairs: <span class=\"katex\"><span class=\"katex-mathml\">4949<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">49<\/span><\/span><\/span><\/span> \u2014 Square root of 49 is <strong data-start=\"1801\" data-end=\"1806\">7<\/strong><br data-start=\"1806\" data-end=\"1809\" \/>Decimal places = 4, so square root will have 2 decimal places.<br data-start=\"1871\" data-end=\"1874\" \/>Answer: <strong data-start=\"1882\" data-end=\"1890\">0.07<\/strong><\/li>\n<\/ul>\n<h3 data-start=\"1897\" data-end=\"1929\"><strong data-start=\"1901\" data-end=\"1927\">\u00a0Practice Questions:<\/strong><\/h3>\n<ol data-start=\"1930\" data-end=\"2059\">\n<li data-start=\"1930\" data-end=\"1953\"><span class=\"katex\"><span class=\"katex-mathml\">361\\sqrt{361}<\/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\">361<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span> = ?<\/li>\n<li data-start=\"1954\" data-end=\"1977\"><span class=\"katex\"><span class=\"katex-mathml\">225\\sqrt{225}<\/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\">225<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span> = ?<\/li>\n<li data-start=\"1978\" data-end=\"2004\"><span class=\"katex\"><span class=\"katex-mathml\">0.0025\\sqrt{0.0025}<\/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\">0.0025<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span> = ?<\/li>\n<li data-start=\"2005\" data-end=\"2037\"><span class=\"katex\"><span class=\"katex-mathml\">18\\sqrt{18}<\/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\">18<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span> (approx.) = ?<\/li>\n<li data-start=\"2038\" data-end=\"2059\"><span class=\"katex\"><span class=\"katex-mathml\">625\\sqrt{625}<\/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\">625<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span> = ?<\/li>\n<\/ol>\n<p data-start=\"2066\" data-end=\"2150\" data-is-last-node=\"\" data-is-only-node=\"\">If you need more detailed methods or have specific questions, just let me know!<\/p>\n<h3 data-start=\"2066\" data-end=\"2150\"><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 ROOT Tricks for Placement tricks.<\/a><\/h3>\n<h3 class=\"LC20lb MBeuO DKV0Md\"><a href=\"https:\/\/teachmint.storage.googleapis.com\/public\/817166298\/StudyMaterial\/6078dc9b-178d-4abf-888b-aa78669af45c.pdf\" target=\"_blank\" rel=\"noopener\">Short tricks to calculate square roots &#8211; googleapis.com<\/a><\/h3>\n<p data-start=\"0\" data-end=\"188\">Sure! Here&#8217;s a <strong data-start=\"15\" data-end=\"71\">collection of super fast and easy square root tricks<\/strong> \u2014 perfect for <strong data-start=\"86\" data-end=\"100\">placements<\/strong>, <strong data-start=\"102\" data-end=\"120\">aptitude tests<\/strong>, and <strong data-start=\"126\" data-end=\"147\">competitive exams<\/strong> like SSC, Bank, Campus Recruitment, etc.<\/p>\n<hr data-start=\"190\" data-end=\"193\" \/>\n<h2 data-start=\"195\" data-end=\"264\">\ud83e\uddee <strong data-start=\"201\" data-end=\"264\">Mathematics Short Tricks: Square Root Tricks for Placements<\/strong><\/h2>\n<hr data-start=\"266\" data-end=\"269\" \/>\n<h3 data-start=\"271\" data-end=\"339\">\u2705 <strong data-start=\"277\" data-end=\"339\">Trick #1: Perfect Square Identification (Last Digit Trick)<\/strong><\/h3>\n<p data-start=\"341\" data-end=\"405\">Check if a number is a <strong data-start=\"364\" data-end=\"382\">perfect square<\/strong> by its <strong data-start=\"390\" data-end=\"404\">last digit<\/strong>.<\/p>\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=\"407\" data-end=\"862\">\n<thead data-start=\"407\" data-end=\"463\">\n<tr data-start=\"407\" data-end=\"463\">\n<th data-start=\"407\" data-end=\"430\" data-col-size=\"sm\">Last Digit of Square<\/th>\n<th data-start=\"430\" data-end=\"463\" data-col-size=\"sm\">Possible Last Digit of Number<\/th>\n<\/tr>\n<\/thead>\n<tbody data-start=\"521\" data-end=\"862\">\n<tr data-start=\"521\" data-end=\"577\">\n<td data-start=\"521\" data-end=\"544\" data-col-size=\"sm\">0<\/td>\n<td data-start=\"544\" data-end=\"577\" data-col-size=\"sm\">0<\/td>\n<\/tr>\n<tr data-start=\"578\" data-end=\"634\">\n<td data-start=\"578\" data-end=\"601\" data-col-size=\"sm\">1<\/td>\n<td data-start=\"601\" data-end=\"634\" data-col-size=\"sm\">1 or 9<\/td>\n<\/tr>\n<tr data-start=\"635\" data-end=\"691\">\n<td data-start=\"635\" data-end=\"658\" data-col-size=\"sm\">4<\/td>\n<td data-start=\"658\" data-end=\"691\" data-col-size=\"sm\">2 or 8<\/td>\n<\/tr>\n<tr data-start=\"692\" data-end=\"748\">\n<td data-start=\"692\" data-end=\"715\" data-col-size=\"sm\">5<\/td>\n<td data-start=\"715\" data-end=\"748\" data-col-size=\"sm\">5<\/td>\n<\/tr>\n<tr data-start=\"749\" data-end=\"805\">\n<td data-start=\"749\" data-end=\"772\" data-col-size=\"sm\">6<\/td>\n<td data-start=\"772\" data-end=\"805\" data-col-size=\"sm\">4 or 6<\/td>\n<\/tr>\n<tr data-start=\"806\" data-end=\"862\">\n<td data-start=\"806\" data-end=\"829\" data-col-size=\"sm\">9<\/td>\n<td data-start=\"829\" data-end=\"862\" data-col-size=\"sm\">3 or 7<\/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<p data-start=\"864\" data-end=\"906\">\ud83d\udd0d <strong data-start=\"867\" data-end=\"879\">Example:<\/strong> Is 784 a perfect square?<\/p>\n<ul data-start=\"907\" data-end=\"969\">\n<li data-start=\"907\" data-end=\"951\">\n<p data-start=\"909\" data-end=\"951\">Last digit is <strong data-start=\"923\" data-end=\"928\">4<\/strong> \u2192 must end in 2 or 8<\/p>\n<\/li>\n<li data-start=\"952\" data-end=\"969\">\n<p data-start=\"954\" data-end=\"969\">\u221a784 = \u2705 <strong data-start=\"963\" data-end=\"969\">28<\/strong><\/p>\n<\/li>\n<\/ul>\n<hr data-start=\"971\" data-end=\"974\" \/>\n<h3 data-start=\"976\" data-end=\"1050\">\u2705 <strong data-start=\"982\" data-end=\"1050\">Trick #2: Find Square Root of a Perfect Square (2-Digit Numbers)<\/strong><\/h3>\n<h4 data-start=\"1052\" data-end=\"1071\">Example: \u221a1521<\/h4>\n<ol data-start=\"1073\" data-end=\"1239\">\n<li data-start=\"1073\" data-end=\"1127\">\n<p data-start=\"1076\" data-end=\"1127\">Last digit = <strong data-start=\"1089\" data-end=\"1094\">1<\/strong>, possible unit digits = 1 or 9<\/p>\n<\/li>\n<li data-start=\"1128\" data-end=\"1183\">\n<p data-start=\"1131\" data-end=\"1183\">Nearest square below 1521 is <strong data-start=\"1160\" data-end=\"1168\">1444<\/strong> \u2192 \u221a1444 = 38<\/p>\n<\/li>\n<li data-start=\"1184\" data-end=\"1239\">\n<p data-start=\"1187\" data-end=\"1196\">Try both:<\/p>\n<ul data-start=\"1200\" data-end=\"1239\">\n<li data-start=\"1200\" data-end=\"1216\">\n<p data-start=\"1202\" data-end=\"1216\">39\u00b2 = 1521 \u2705<\/p>\n<\/li>\n<li data-start=\"1220\" data-end=\"1239\">\n<p data-start=\"1222\" data-end=\"1239\">So \u221a1521 = <strong data-start=\"1233\" data-end=\"1239\">39<\/strong><\/p>\n<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<hr data-start=\"1241\" data-end=\"1244\" \/>\n<h3 data-start=\"1246\" data-end=\"1300\">\u2705 <strong data-start=\"1252\" data-end=\"1300\">Trick #3: Estimation for Non-Perfect Squares<\/strong><\/h3>\n<h4 data-start=\"1302\" data-end=\"1319\">Example: \u221a50<\/h4>\n<ul data-start=\"1321\" data-end=\"1427\">\n<li data-start=\"1321\" data-end=\"1368\">\n<p data-start=\"1323\" data-end=\"1368\">Perfect squares around 50: \u221a49 = 7, \u221a64 = 8<\/p>\n<\/li>\n<li data-start=\"1369\" data-end=\"1391\">\n<p data-start=\"1371\" data-end=\"1391\">So \u221a50 \u2248 7.0 \u2013 7.1<\/p>\n<\/li>\n<li data-start=\"1392\" data-end=\"1427\">\n<p data-start=\"1394\" data-end=\"1427\">Try 7.1\u00b2 = 50.41 \u2192 Close enough \u2705<\/p>\n<\/li>\n<\/ul>\n<p data-start=\"1429\" data-end=\"1474\">\ud83d\udccc Use this for <strong data-start=\"1445\" data-end=\"1465\">quick estimation<\/strong> in MCQs.<\/p>\n<hr data-start=\"1476\" data-end=\"1479\" \/>\n<h3 data-start=\"1481\" data-end=\"1538\">\u2705 <strong data-start=\"1487\" data-end=\"1538\">Trick #4: Square Root of Numbers Ending with 25<\/strong><\/h3>\n<p data-start=\"1540\" data-end=\"1548\">Formula:<\/p>\n<blockquote data-start=\"1549\" data-end=\"1613\">\n<p data-start=\"1551\" data-end=\"1613\">\u221a(x\u00d7100 + 25) = 10x + 5, <strong data-start=\"1576\" data-end=\"1613\">if the number is a perfect square<\/strong><\/p>\n<\/blockquote>\n<h4 data-start=\"1615\" data-end=\"1636\">Example: \u221a1225<\/h4>\n<ul data-start=\"1637\" data-end=\"1698\">\n<li data-start=\"1637\" data-end=\"1663\">\n<p data-start=\"1639\" data-end=\"1663\">1225 = (12 \u00d7 100 + 25)<\/p>\n<\/li>\n<li data-start=\"1664\" data-end=\"1698\">\n<p data-start=\"1666\" data-end=\"1698\">So \u221a1225 = 10\u00d712 + 5 = \u2705 <strong data-start=\"1691\" data-end=\"1698\">125<\/strong><\/p>\n<\/li>\n<\/ul>\n<hr data-start=\"1700\" data-end=\"1703\" \/>\n<h3 data-start=\"1705\" data-end=\"1754\">\u2705 <strong data-start=\"1711\" data-end=\"1754\">Trick #5: For Square Roots of Fractions<\/strong><\/h3>\n<blockquote data-start=\"1756\" data-end=\"1774\">\n<p data-start=\"1758\" data-end=\"1774\">\u221a(a\/b) = \u221aa \/ \u221ab<\/p>\n<\/blockquote>\n<h4 data-start=\"1776\" data-end=\"1820\">Example: \u221a(49\/16) = \u221a49 \/ \u221a16 = 7 \/ 4 \u2705<\/h4>\n<hr data-start=\"1822\" data-end=\"1825\" \/>\n<h2 data-start=\"1827\" data-end=\"1856\">\ud83e\udde0 <strong data-start=\"1833\" data-end=\"1856\">Practice Questions:<\/strong><\/h2>\n<ol data-start=\"1858\" data-end=\"1955\">\n<li data-start=\"1858\" data-end=\"1872\">\n<p data-start=\"1861\" data-end=\"1872\">\u221a2025 = ?<\/p>\n<\/li>\n<li data-start=\"1873\" data-end=\"1887\">\n<p data-start=\"1876\" data-end=\"1887\">\u221a1369 = ?<\/p>\n<\/li>\n<li data-start=\"1888\" data-end=\"1926\">\n<p data-start=\"1891\" data-end=\"1926\">Which is closer to \u221a82: 9 or 9.1?<\/p>\n<\/li>\n<li data-start=\"1927\" data-end=\"1955\">\n<p data-start=\"1930\" data-end=\"1955\">Is 9801 a perfect square?<\/p>\n<\/li>\n<\/ol>\n<hr data-start=\"1957\" data-end=\"1960\" \/>\n<h2 data-start=\"1962\" data-end=\"1978\">\ud83d\udce6 Want More?<\/h2>\n<p data-start=\"1980\" data-end=\"1994\">I can provide:<\/p>\n<ul data-start=\"1995\" data-end=\"2088\">\n<li data-start=\"1995\" data-end=\"2033\">\n<p data-start=\"1997\" data-end=\"2033\">\ud83d\udcc4 PDF of these tricks with examples<\/p>\n<\/li>\n<li data-start=\"2034\" data-end=\"2056\">\n<p data-start=\"2036\" data-end=\"2056\">\ud83c\udfa5 Video explanation<\/p>\n<\/li>\n<li data-start=\"2057\" data-end=\"2088\">\n<p data-start=\"2059\" data-end=\"2088\">\ud83e\udde0 Quiz on square root tricks<\/p>\n<\/li>\n<\/ul>\n<p data-start=\"2090\" data-end=\"2129\" data-is-last-node=\"\" data-is-only-node=\"\">Let me know how you\u2019d like to practice!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Mathematics Short Tricks\/ SQUARE ROOT Tricks for Placement tricks. [fvplayer id=&#8221;654&#8243;] Square Root Tricks for Quick Calculation &#8211; Placement Exam Tips \u00a0What is a Square Root? The square root of a number x is a number y such that y2=xy^2 = xy2=x.Example:25=5\\sqrt{25} = 525\u200b=5 because 52=255^2 = 2552=25. Square Root Short Tricks for Quick Calculation: [&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-4199","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\/4199","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=4199"}],"version-history":[{"count":0,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/4199\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/media?parent=4199"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/categories?post=4199"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/tags?post=4199"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}