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It also highlights the simplification of expressions involving roots, showing how exponent and radical forms connect to the same numerical values, supporting fast recall and pattern recognition during practice.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/math-facts-for-the-shsat-patterns-of-perfect-squares-and-square-roots/274383/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/math-facts-for-the-shsat-patterns-of-perfect-squares-and-square-roots/274383.png","ImageObject",300,407,{"name":42,"@type":43},"Lucas Vance","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-22","2026-09-15",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",12,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What range of numbers does the table cover for perfect squares and square roots?","Question",{"text":63,"@type":64},"It covers perfect squares and related square-root patterns for integers from 1 to 25.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"Does the material include both positive and negative square roots?",{"text":68,"@type":64},"Yes. For each square, it shows the ± form, indicating both positive and negative roots.",{"name":70,"@type":61,"acceptedAnswer":71},"What math relationships are emphasized in the table?",{"text":72,"@type":64},"The table emphasizes how squaring and square roots connect, and how expressions involving roots simplify to the corresponding square values.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},274383,1789476792,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,110,115,120,123,127],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & 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\u003Cbr>1 \u003Cbr>1\u003Cbr>= \u003Cbr>112 = \u003Cbr>±1  − 12  = \u003Cbr>− 1 \u003Cbr>− 1\u003Cbr>= \u003Cbr>1 − 12 =\u003Cbr>\u003Cbr>− 1 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| 22 | = | ( -2)2 | = | \u003Cbr>4 | \u003Cbr>| = | \u003Cbr>142 | = | \u003Cbr>±2 | -22 | = |  − 4 | \u003Cbr>| = | \u003Cbr>1 − 42 | = |  − 2 |\n| 32 | = | ( -3)2 | = | \u003Cbr>9 | \u003Cbr>| = | \u003Cbr>192 | = | \u003Cbr>±3 | -32 | = |  − 9 | \u003Cbr>| = | \u003Cbr>1 − 92 | = |  − 3 |\n| 42 | = | ( -4)2 | = | \u003Cbr>16 | \u003Cbr>16\u003Cbr>| = | \u003Cbr>1\u003Cbr>162 | = | \u003Cbr>±4 | -42 | = | \u003Cbr>− 16 | \u003Cbr>−\u003Cbr>169\u003Cbr>| = | \u003Cbr>1 − 162 | = |  − 4 |\n| 52 | = | ( -5)2 | = | \u003Cbr>25 | \u003Cbr>25\u003Cbr>| = | \u003Cbr>1252 | = | \u003Cbr>±5 | -52 | = | \u003Cbr>− 25 | \u003Cbr>−\u003Cbr>25\u003Cbr>| = | \u003Cbr>1 − 252 | = |  − 5 |\n| 62 | = | ( -6)2 | = | \u003Cbr>36 | \u003Cbr>36\u003Cbr>| = | \u003Cbr>1362 | = | \u003Cbr>±6 | -62 | = | \u003Cbr>− 36 | \u003Cbr>−\u003Cbr>36\u003Cbr>| = | \u003Cbr>1 − 362 | = |  − 6 |\n| 72 | = | ( -7)2 | = | \u003Cbr>49 | \u003Cbr>49\u003Cbr>| = | \u003Cbr>1492 | = | \u003Cbr>±7 | -72 | = | \u003Cbr>− 49 | \u003Cbr>−\u003Cbr>49\u003Cbr>| = | \u003Cbr>1 − 492 | = |  − 7 |\n| 82 | = | ( -8)2 | = | \u003Cbr>64 | \u003Cbr>64\u003Cbr>| = | \u003Cbr>1642 | = | \u003Cbr>±8 | -82 | = | \u003Cbr>− 64 | \u003Cbr>−\u003Cbr>64\u003Cbr>| = | \u003Cbr>1 − 642 | = |  − 8 |\n| 92 | = | ( -9)2 | = | \u003Cbr>81 | \u003Cbr>81\u003Cbr>| = | \u003Cbr>1\u003Cbr>812 | = | \u003Cbr>±9 | -92 | = | \u003Cbr>− 81 | \u003Cbr>− 81\u003Cbr>| = | \u003Cbr>1 − 812 | = | \u003Cbr>− 9 |\n| 102 | = | ( -10)2 | = | 100 |  100 \u003Cbr>| = | \u003Cbr>11002 | = | \u003Cbr>±10 | -102 | = | \u003Cbr>− 100 | \u003Cbr>−\u003Cbr>100\u003Cbr>| = | \u003Cbr>1 − 1002 | = | \u003Cbr>− 10 |\n| 112 | = | ( -11)2 | = | 121 |  121\u003Cbr>| = | \u003Cbr>11212 | = | \u003Cbr>±11 | -112 | = | \u003Cbr>− 121 | \u003Cbr>−\u003Cbr>121\u003Cbr>| = | \u003Cbr>1 − 1212 | = | \u003Cbr>− 11 |\n| 122 | = | ( -12)2 | = | 144 |  144 \u003Cbr>| = | \u003Cbr>11442 | = | \u003Cbr>±12 | -122 | = | \u003Cbr>− 144 | \u003Cbr>−\u003Cbr>144\u003Cbr>| = | \u003Cbr>1 − 1442 | = | \u003Cbr>− 12 |\n| 132 | = | ( -13)2 | = | 169 |  169 \u003Cbr>| = | \u003Cbr>11692 | = | \u003Cbr>±13 | -132 | = | \u003Cbr>− 169 | \u003Cbr>−\u003Cbr>169\u003Cbr>| = | \u003Cbr>1 − 1692 | = | \u003Cbr>− 13 |\n| 142 | = | ( -14)2 | = | 196 |  196 \u003Cbr>| = | \u003Cbr>11962 | = | \u003Cbr>±14 | -142 | = | \u003Cbr>− 196 | \u003Cbr>−\u003Cbr>196\u003Cbr>| = | \u003Cbr>1 − 1962 | = | \u003Cbr>− 14 |\n| 152 | = | ( -15)2 | = | 225 |  225\u003Cbr>| = | \u003Cbr>12252 | = | \u003Cbr>±15 | -152 | = | \u003Cbr>− 225 | \u003Cbr>−\u003Cbr>225\u003Cbr>| = | \u003Cbr>1 − 2252 | = | \u003Cbr>− 15 |\n| 162 | = | ( -16)2 | = | 256 |  256\u003Cbr>| = | \u003Cbr>12562 | = | \u003Cbr>±16 | -162 | = | \u003Cbr>− 256 | \u003Cbr>−\u003Cbr>256\u003Cbr>| = | \u003Cbr>1 − 2562 | = | \u003Cbr>− 16 |\n| 172 | = | ( -17)2 | = | 289 |  289\u003Cbr>| = | \u003Cbr>12892 | = | \u003Cbr>±17 | -172 | = | \u003Cbr>− 289 | \u003Cbr>−\u003Cbr>289\u003Cbr>| = | \u003Cbr>1 − 2892 | = | \u003Cbr>− 17 |\n| 182 | = | ( -18)2 | = | 324 |  324\u003Cbr>| = | \u003Cbr>13242 | = | \u003Cbr>±18 | -182 | = | \u003Cbr>− 324 | \u003Cbr>−\u003Cbr>324\u003Cbr>| = | \u003Cbr>1 − 3242 | = | \u003Cbr>− 18 |\n| 192 | = | ( -19)2 | = | 361 |  361\u003Cbr>| = | \u003Cbr>13612 | = | \u003Cbr>±19 | -192 | = | \u003Cbr>− 361 | \u003Cbr>−\u003Cbr>361\u003Cbr>| = | \u003Cbr>1 − 3612 | = | \u003Cbr>− 19 |\n| 202 | = | ( -20)2 | = | 400 |  400\u003Cbr>| = | \u003Cbr>14002 | = | \u003Cbr>±20 | -202 | = | \u003Cbr>− 400 | \u003Cbr>−\u003Cbr>400\u003Cbr>| = | \u003Cbr>1 − 4002 | = | \u003Cbr>− 20 |\n| 212 | = | ( -21)2 | = | 441 |  441\u003Cbr>| = | \u003Cbr>14412 | = | \u003Cbr>±21 | -212 | = | \u003Cbr>− 441 | \u003Cbr>−\u003Cbr>441\u003Cbr>| = | \u003Cbr>1 − 4412 | = | \u003Cbr>− 21 |\n| 222 | = | ( -22)2 | = | 484 |  484\u003Cbr>| = | \u003Cbr>14842 | = | \u003Cbr>±22 | -222 | = | \u003Cbr>− 484 | \u003Cbr>−\u003Cbr>484\u003Cbr>| = | \u003Cbr>1 − 4842 | = | \u003Cbr>− 22 |\n| 232 | = | ( -23)2 | = | 529 |  529\u003Cbr>| = | \u003Cbr>15292 | = | \u003Cbr>±23 | -232 | = | \u003Cbr>− 529 | \u003Cbr>−\u003Cbr>529\u003Cbr>| = | \u003Cbr>1 − 5292 | = | \u003Cbr>− 23 |\n| 242 | = | ( -24)2 | = | 576 |  576\u003Cbr>| = | \u003Cbr>15762 | = | \u003Cbr>±24 | -242 | = | \u003Cbr>− 576 | \u003Cbr>−\u003Cbr>576\u003Cbr>| = | \u003Cbr>1 − 5762 | = | \u003Cbr>− 24 |\n| 252 | = | ( -25)2 | = | 625 |  625\u003Cbr>| = | \u003Cbr>16252 | = | \u003Cbr>±25 |  − 252  | = | \u003Cbr>− 625 | \u003Cbr>−\u003Cbr>625\u003Cbr>| = | \u003Cbr>1 − 6252 | = | \u003Cbr>− 25 |\n\n© 2020 Allannah Thomas 8","cbCaiv6ZtG4HYPLa","https://ap.wps.com/l/cbCaiv6ZtG4HYPLa","pdf",2212712,"English","# Patterns of Perfect Squares and Square Roots (1 - 25)","[{\"question\":\"What range of numbers does the table cover for perfect squares and square roots?\",\"answer\":\"It covers perfect squares and related square-root patterns for integers from 1 to 25.\"},{\"question\":\"Does the material include both positive and negative square roots?\",\"answer\":\"Yes. For each square, it shows the ± form, indicating both positive and negative roots.\"},{\"question\":\"What math relationships are emphasized in the table?\",\"answer\":\"The table emphasizes how squaring and square roots connect, and how expressions involving roots simplify to the corresponding square values.\"}]","Math Facts for the SHSAT - Patterns of Perfect Squares and Square Roots | PDF"]