[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-274530-105":59,"doc-detail-274530-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","chang-learning-shsat-lesson-4-square-roots","Chang Learning SHSAT Lesson - 4 - Square Roots","","SHSAT Mathematics Lesson #4 focuses on square roots, starting from the relationship between a square’s area and the side length. The lesson builds mastery of perfect squares up to 20, explains how to locate whole-number square roots, and shows how to approximate non-perfect-square radicals using nearby perfect squares. It also practices arithmetic with radicals, including multiplying, dividing, and simplifying expressions, followed by SHSAT-style classwork and exam questions.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/chang-learning-shsat-lesson-4-square-roots/274530/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/chang-learning-shsat-lesson-4-square-roots/274530.png","ImageObject",300,407,{"name":92,"@type":93},"Alex Sinclair","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-22","2026-09-15",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",15,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"How do you find a square root from a square’s area?","Question",{"text":113,"@type":114},"For a square, the square root equals the length of the side. For example, if the area is 25 square units, the side length is √25 = 5.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What should you do if a number is not a perfect square?",{"text":118,"@type":114},"Find the two perfect squares that the number lies between, then estimate. For instance, 67 lies between 64 and 81, so √67 is between 8 and 9.",{"name":120,"@type":111,"acceptedAnswer":121},"How are radicals handled in operations like multiplication and division?",{"text":122,"@type":114},"Radicals can be multiplied and combined by multiplying inside terms, and division can be handled similarly by separating factors. The lesson includes practice such as simplifying products of radicals.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},274530,1789478415,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":140,"language":141,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":67,"update_tm":130,"read_time":41},1099523882182,"https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","Name: Date:  \nChang Learning SHSAT Lesson \\#4: Square Roots  \nSquare Roots  \nWhen a square, let’s call it Square Q, has Area A , the square root is the length of the side of Square Q. For example. If Square Q equals 25 square units, then the length of the side of Square Q is 5.  \nIt’s good to know your squares up to 20 for the SHSAT. Most problems in middle school mathematics use squares from 1 to 10, but this test often makes the work a little more challenging for the learner by extending this list up to 20.  \n\n| n | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| 􀕗2 | 1 | 4 | 9 | 16 | 25 | 36 | 49 | 64 | 81 | 100 |\n\n\n| n | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| 􀕗2 | 121 | 144 | 169 | 196 | 225 | 256 | 289 | 324 | 361 | 400 |\n\nIf you know your squares, then the inverse operation of squaring “n” is to take the square root of a number “n”. This list has spaces between the natural numbers, the skips between perfect squares, that increase by odd values.  \n\n| n | 1 | 4 | 9 | 16 | 25 | 36 | 49 | 64 | 81 | 100 |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| 􀕗\u003Cbr>| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |\n\n\n| n | 121 | 144 | 169 | 196 | 225 | 256 | 289 | 324 | 361 | 400 |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| 􀕗\u003Cbr>| 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |\n\nFrom this list we know that:  \nThese are square roots that are perfect squares: 4 = 2. 100 = 10. 361 = 19. These values of “n” have square roots that are whole number values.  \nWhat if it is NOT a perfect square ? What two whole numbers is the positive square root close to ?  \n| 10\u003Cbr>| We know 9 \u003C 10 \u003C 16. Therefore 3 \u003C 10 \u003C 4\u003Cbr>| Between 3 and 4 . |\n| --- | --- | --- |\n| 67\u003Cbr>| We know 64 \u003C 67 \u003C 81. Therefore 8 \u003C 67 \u003C 9\u003Cbr>| Between 8 and 9. |\n| 173\u003Cbr>| We know 169 \u003C 173 \u003C 196. Therefore 13 \u003C 173 \u003C 14\u003Cbr>| Between 13 and 14. |\n\nSHSAT Mathematics Lesson \\#4 Page 1  \nName: Date:  \nChang Learning SHSAT Lesson \\#4: Square Roots  \nIt also helps to know that radicals that are NOT perfect squares can be approximated with these known perfect squares.  \n24 􀕒􀕜 􀕌􀕕􀕘􀕜􀕎 􀕝􀕘 25 = 5. 􀕃ℎ􀕎􀕛􀕎􀕏􀕘􀕛􀕎 5 􀕒􀕜 􀕊 􀕐􀕘􀕘􀕍 􀕎􀕜􀕝􀕒􀕖􀕊􀕝􀕎 􀕏􀕘􀕛 24.  \n120 􀕒􀕜 􀕌􀕕􀕘􀕜􀕎 􀕝􀕘 121 = 11. 􀕃ℎ􀕎􀕛􀕎􀕏􀕘􀕛􀕎 11 􀕒􀕜 􀕊 􀕐􀕘􀕘􀕍 􀕎􀕜􀕝􀕒􀕖􀕊􀕝􀕎 􀕏􀕘􀕛 120.  \nAlthough classroom lessons have square roots that usually measure from 1 􀕝􀕘 100 , it is not uncommon to see three digit square roots on the SHSAT!  \n| 400 − 289 = 20 − 17 = 3.\u003Cbr>|\n| --- |\n| 225 − 36 = 15 − 6 = 9.\u003Cbr>|\n| 16 + 49 = 4 + 7 = 11.\u003Cbr>|\n\nRadicals can also be multiplied and divided:  \n\n| 􀕊 * 􀕋 = 􀕊􀕋\u003Cbr>|  |  | 6 * 2 = 12\u003Cbr>2 * 3 = 6\u003Cbr>6 * 2 * 3 = 36 = 6\u003Cbr>\u003Cbr>\u003Cbr>|\n| --- | --- | --- | --- |\n| | = |  􀕊 􀕋\u003Cbr>\u003Cbr>| 9  9  3 = =\u003Cbr>4 4 2\u003Cbr>\u003Cbr>\u003Cbr>\u003Cbr>|\n\nSHSAT Mathematics Lesson \\#4 Page 2  \nName: Date:  \nChang Learning SHSAT Lesson \\#4: Square Roots  \nSHSAT Lesson \\#4 Classwork: Square Roots  \n\n| 1. 225 + 36 =\u003Cbr>| A. 18\u003Cbr>B. 19\u003Cbr>C. 20\u003Cbr>D. 21\u003Cbr>E. 22 |\n| --- | --- |\n| 2. 25 − 400 =\u003Cbr>| A. 10\u003Cbr>B. 11\u003Cbr>C. 12\u003Cbr>D. 13\u003Cbr>E. 14 |\n| 3. 4225~~ ~~  | A  2 . 25\u003Cbr> 4  B.\u003Cbr>25 C. ~~ ~~25~~ ~~\u003Cbr> 4  D.\u003Cbr>5\u003Cbr> 16  E\u003Cbr>. 5 |\n| 4. 81 =\u003Cbr>| A. 81\u003Cbr>B. 54\u003Cbr>C. 36\u003Cbr>D. 27\u003Cbr>E. 3 |\n| 5. If N = 36 + 49, 􀕝ℎ􀕎􀕗 􀔽 􀕒􀕜\u003Cbr>| A. A number between 9 and 10 B. A number between 10 and 11 C. A number between 11 and 12 D. A number between 12 and 13 E. 13 |\n| 6. 36 * 9 + 16 =\u003Cbr>| A. ~~ ~~ 340 B. 22\u003Cbr>C. 30\u003Cbr>D. 42\u003Cbr>E. 150\u003Cbr>|\n\nSHSAT Mathematics Lesson \\#4 Page 3  \nName: Date:  \nChang Learning SHSAT Lesson \\#4: Square Roots  \nSHSAT Lesson \\#4: Classwork (continued)  \n\n| 7. The exact value of 36 + 5 􀕒􀕜\u003Cbr>|  |  | A. Between 6 and 7\u003Cbr>B. Between 7 and 8\u003Cbr>C. Between 8 and 9\u003Cbr>D. Between 9 and 10 E. Between 10 and 11 |\n| --- | --- | --- | --- |\n| 8. If 32􀕡 = 81, then x =\u003Cbr>|  |  | A. 1\u003Cbr>B. 2\u003Cbr>C. 3\u003Cbr>D. 0.5\u003Cbr>E. None of the above. |\n| 9. 157 is\u003Cbr>|  |  | A. Between 11 and 12 B. Between 12 and","cbCaik943B8HINcW","https://ap.wps.com/l/cbCaik943B8HINcW","pdf",171044,12,"English","# Square Roots\n## Perfect Squares and Whole-Number Roots\n## Approximating Non-Perfect-Square Radicals\n## Operations with Radicals\n## SHSAT Lesson №4 Classwork\n## SHSAT Exam Classwork","[{\"question\":\"How do you find a square root from a square’s area?\",\"answer\":\"For a square, the square root equals the length of the side. For example, if the area is 25 square units, the side length is √25 = 5.\"},{\"question\":\"What should you do if a number is not a perfect square?\",\"answer\":\"Find the two perfect squares that the number lies between, then estimate. For instance, 67 lies between 64 and 81, so √67 is between 8 and 9.\"},{\"question\":\"How are radicals handled in operations like multiplication and division?\",\"answer\":\"Radicals can be multiplied and combined by multiplying inside terms, and division can be handled similarly by separating factors. The lesson includes practice such as simplifying products of radicals.\"}]","Chang Learning SHSAT Lesson - 4 - Square Roots | PDF"]