{"id":15613,"date":"2021-10-17T00:58:50","date_gmt":"2021-10-17T00:58:50","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/?post_type=chapter&#038;p=15613"},"modified":"2022-02-05T00:54:20","modified_gmt":"2022-02-05T00:54:20","slug":"problem-set-square-roots","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/chapter\/problem-set-square-roots\/","title":{"raw":"Problem set: Square roots","rendered":"Problem set: Square roots"},"content":{"raw":"<strong>Simplify Expressions with Square Roots<\/strong>\r\n\r\nIn the following exercises, simplify.\r\n<ol>\r\n \t<li style=\"list-style-type: none;\">\r\n<ol>\r\n \t<li>[latex]\\sqrt{36}[\/latex]\r\n[reveal-answer q=\"401551\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"401551\"]6[\/hidden-answer]<\/li>\r\n \t<li>[latex]\\sqrt{4}[\/latex]<\/li>\r\n \t<li>[latex]\\sqrt{64}[\/latex]\r\n[reveal-answer q=\"157868\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"157868\"]8[\/hidden-answer]<\/li>\r\n \t<li>[latex]\\sqrt{144}[\/latex]<\/li>\r\n \t<li>[latex]-\\sqrt{4}[\/latex]\r\n[reveal-answer q=\"607127\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"607127\"]\u22122[\/hidden-answer]<\/li>\r\n \t<li>[latex]-\\sqrt{100}[\/latex]<\/li>\r\n \t<li>[latex]-\\sqrt{1}[\/latex]\r\n[reveal-answer q=\"273460\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"273460\"]\u22121[\/hidden-answer]<\/li>\r\n \t<li>[latex]-\\sqrt{121}[\/latex]<\/li>\r\n \t<li>[latex]\\sqrt{-121}[\/latex]\r\n[reveal-answer q=\"141775\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"141775\"]not a real number[\/hidden-answer]<\/li>\r\n \t<li>[latex]\\sqrt{-36}[\/latex]<\/li>\r\n \t<li>[latex]\\sqrt{-9}[\/latex]\r\n[reveal-answer q=\"227141\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"227141\"]not a real number[\/hidden-answer]<\/li>\r\n \t<li>[latex]\\sqrt{-49}[\/latex]<\/li>\r\n \t<li>[latex]\\sqrt{9+16}[\/latex]\r\n[reveal-answer q=\"177779\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"177779\"]5[\/hidden-answer]<\/li>\r\n \t<li>[latex]\\sqrt{25+144}[\/latex]<\/li>\r\n \t<li>[latex]\\sqrt{9}+\\sqrt{16}[\/latex]\r\n[reveal-answer q=\"652944\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"652944\"]7[\/hidden-answer]<\/li>\r\n \t<li>[latex]\\sqrt{25}+\\sqrt{144}[\/latex]<\/li>\r\n \t<li>[latex]\\sqrt{64}[\/latex]<\/li>\r\n \t<li>[latex]\\sqrt{144}[\/latex]\r\n[reveal-answer q=\"963585\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"963585\"]12[\/hidden-answer]<\/li>\r\n \t<li>[latex]-\\sqrt{25}[\/latex]<\/li>\r\n \t<li>[latex]-\\sqrt{81}[\/latex]\r\n[reveal-answer q=\"189244\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"189244\"]\u22129[\/hidden-answer]<\/li>\r\n \t<li>[latex]\\sqrt{-9}[\/latex]<\/li>\r\n \t<li>[latex]\\sqrt{-36}[\/latex]\r\n[reveal-answer q=\"234775\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"234775\"]not a real number[\/hidden-answer]<\/li>\r\n \t<li>[latex]\\sqrt{64}+\\sqrt{225}[\/latex]<\/li>\r\n \t<li>[latex]\\sqrt{64+225}[\/latex]\r\n[reveal-answer q=\"766462\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"766462\"]17[\/hidden-answer]<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n<h3><strong>Estimate Square Roots<\/strong><\/h3>\r\nIn the following exercises, estimate each square root between two consecutive whole numbers.\r\n<ol>\r\n \t<li style=\"list-style-type: none;\">\r\n<ol>\r\n \t<li>[latex]\\sqrt{70}[\/latex]\r\n[reveal-answer q=\"294230\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"294230\"][latex]8&lt;\\sqrt{70}&lt;9[\/latex][\/hidden-answer]<\/li>\r\n \t<li>[latex]\\sqrt{55}[\/latex]<\/li>\r\n \t<li>[latex]\\sqrt{200}[\/latex]\r\n[reveal-answer q=\"159114\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"159114\"][latex]14&lt;\\sqrt{200}&lt;15[\/latex][\/hidden-answer]<\/li>\r\n \t<li>[latex]\\sqrt{172}[\/latex]<\/li>\r\n \t<li>[latex]\\sqrt{28}[\/latex]<\/li>\r\n \t<li>[latex]\\sqrt{155}[\/latex]\r\n[reveal-answer q=\"454994\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"454994\"][latex]12&lt;\\sqrt{155}&lt;13[\/latex][\/hidden-answer]<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n<h3><strong>Approximate Square Roots with a Calculator<\/strong><\/h3>\r\nIn the following exercises, use a calculator to approximate each square root and round to two decimal places.\r\n<ol>\r\n \t<li style=\"list-style-type: none;\">\r\n<ol>\r\n \t<li>[latex]\\sqrt{19}[\/latex]\r\n[reveal-answer q=\"35646\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"35646\"]4.36[\/hidden-answer]<\/li>\r\n \t<li>[latex]\\sqrt{21}[\/latex]<\/li>\r\n \t<li>[latex]\\sqrt{53}[\/latex]\r\n[reveal-answer q=\"758190\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"758190\"]7.28[\/hidden-answer]<\/li>\r\n \t<li>[latex]\\sqrt{47}[\/latex]<\/li>\r\n \t<li>[latex]\\sqrt{15}[\/latex]<\/li>\r\n \t<li>[latex]\\sqrt{57}[\/latex]\r\n[reveal-answer q=\"266393\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"266393\"]7.55[\/hidden-answer]<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n<h3><strong>Simplify Variable Expressions with Square Roots<\/strong><\/h3>\r\nIn the following exercises, simplify. (Assume all variables are greater than or equal to zero.)\r\n<ol>\r\n \t<li style=\"list-style-type: none;\">\r\n<ol>\r\n \t<li>[latex]\\sqrt{{y}^{2}}[\/latex]\r\n[reveal-answer q=\"695747\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"695747\"]y[\/hidden-answer]<\/li>\r\n \t<li>[latex]\\sqrt{{b}^{2}}[\/latex]<\/li>\r\n \t<li>[latex]\\sqrt{49{x}^{2}}[\/latex]\r\n[reveal-answer q=\"958230\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"958230\"]7x[\/hidden-answer]<\/li>\r\n \t<li>[latex]\\sqrt{100{y}^{2}}[\/latex]<\/li>\r\n \t<li>[latex]-\\sqrt{64{a}^{2}}[\/latex]\r\n[reveal-answer q=\"91775\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"91775\"]\u22128a[\/hidden-answer]<\/li>\r\n \t<li>[latex]-\\sqrt{25{x}^{2}}[\/latex]<\/li>\r\n \t<li>[latex]\\sqrt{144{x}^{2}{y}^{2}}[\/latex]\r\n[reveal-answer q=\"299115\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"299115\"]12xy[\/hidden-answer]<\/li>\r\n \t<li>[latex]\\sqrt{196{a}^{2}{b}^{2}}[\/latex]<\/li>\r\n \t<li>[latex]\\sqrt{{q}^{2}}[\/latex]<\/li>\r\n \t<li>[latex]\\sqrt{64{b}^{2}}[\/latex]\r\n[reveal-answer q=\"503702\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"503702\"]8b[\/hidden-answer]<\/li>\r\n \t<li>[latex]-\\sqrt{121{a}^{2}}[\/latex]<\/li>\r\n \t<li>[latex]\\sqrt{225{m}^{2}{n}^{2}}[\/latex]\r\n[reveal-answer q=\"646234\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"646234\"]15mn[\/hidden-answer]<\/li>\r\n \t<li>[latex]-\\sqrt{100{q}^{2}}[\/latex]<\/li>\r\n \t<li>[latex]\\sqrt{49{y}^{2}}[\/latex]\r\n[reveal-answer q=\"419424\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"419424\"]7y[\/hidden-answer]<\/li>\r\n \t<li>[latex]\\sqrt{4{a}^{2}{b}^{2}}[\/latex]<\/li>\r\n \t<li>[latex]\\sqrt{121{c}^{2}{d}^{2}}[\/latex]\r\n[reveal-answer q=\"929578\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"929578\"]11cd[\/hidden-answer]<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n<h3><strong>Use Square Roots in Applications<\/strong><\/h3>\r\nIn the following exercises, solve. Round to one decimal place.\r\n\r\n<strong>Landscaping<\/strong> Reed wants to have a square garden plot in his backyard. He has enough compost to cover an area of [latex]75[\/latex] square feet. How long can a side of his garden be?\r\n<ol>\r\n \t<li style=\"list-style-type: none;\">\r\n<ol>[reveal-answer q=\"677415\"]Show Solution[\/reveal-answer]<\/ol>\r\n<\/li>\r\n<\/ol>\r\n<ol>\r\n \t<li style=\"list-style-type: none;\">\r\n<ol>[hidden-answer a=\"677415\"]8.7 feet[\/hidden-answer]<\/ol>\r\n<\/li>\r\n<\/ol>\r\n<strong>Landscaping<\/strong> Vince wants to make a square patio in his yard. He has enough concrete to pave an area of 130 square feet. How long can a side of his patio be?\r\n\r\n<strong>Gravity<\/strong> An airplane dropped a flare from a height of 1,024 feet above a lake. How many seconds did it take for the flare to reach the water?\r\n<ol>\r\n \t<li style=\"list-style-type: none;\">\r\n<ol>[reveal-answer q=\"585839\"]Show Solution[\/reveal-answer]<\/ol>\r\n<\/li>\r\n<\/ol>\r\n<ol>\r\n \t<li style=\"list-style-type: none;\">\r\n<ol>[hidden-answer a=\"585839\"]8 seconds[\/hidden-answer]<\/ol>\r\n<\/li>\r\n<\/ol>\r\n<strong>Gravity <\/strong>A hiker dropped a granola bar from a lookout spot 576 feet above a valley. How long did it take the granola bar to reach the valley floor?\r\n\r\n<strong>Gravity<\/strong> A hang glider dropped his cell phone from a height of 350 feet. How many seconds did it take for the cell phone to reach the ground?\r\n\r\n<strong>Gravity<\/strong> A construction worker dropped a hammer while building the Grand Canyon skywalk, 4,000 feet above the Colorado River. How many seconds did it take for the hammer to reach the river?\r\n<ol>\r\n \t<li style=\"list-style-type: none;\">\r\n<ol>[reveal-answer q=\"550466\"]Show Solution[\/reveal-answer]<\/ol>\r\n<\/li>\r\n<\/ol>\r\n<ol>\r\n \t<li style=\"list-style-type: none;\">\r\n<ol>[hidden-answer a=\"550466\"]15.8 seconds[\/hidden-answer]<\/ol>\r\n<\/li>\r\n<\/ol>\r\n<strong>Accident investigation<\/strong> The skid marks from a car involved in an accident measured 54 feet. What was the speed of the car before the brakes were applied?\r\n\r\n<strong>Accident investigation<\/strong> The skid marks from a car involved in an accident measured 216 feet. What was the speed of the car before the brakes were applied?\r\n<ol>\r\n \t<li style=\"list-style-type: none;\">\r\n<ol>[reveal-answer q=\"353928\"]Show Solution[\/reveal-answer]<\/ol>\r\n<ol>[hidden-answer a=\"353928\"]72 mph[\/hidden-answer]<\/ol>\r\n<\/li>\r\n<\/ol>\r\n<strong>Accident investigation<\/strong> An accident investigator measured the skid marks of one of the vehicles involved in an accident. The length of the skid marks was 175 feet. What was the speed of the vehicle before the brakes were applied?\r\n\r\n<strong>Accident investigation<\/strong> An accident investigator measured the skid marks of one of the vehicles involved in an accident. The length of the skid marks was 117 feet. What was the speed of the vehicle before the brakes were applied?\r\n<ol>\r\n \t<li style=\"list-style-type: none;\">\r\n<ol>[reveal-answer q=\"875333\"]Show Solution[\/reveal-answer]<\/ol>\r\n<ol>[hidden-answer a=\"875333\"]53.0 mph[\/hidden-answer]<\/ol>\r\n<\/li>\r\n \t<li style=\"list-style-type: none;\">\r\n<div class=\"textbox exercises\">\r\n<h3>Everyday Math<\/h3>\r\n<ol>\r\n \t<li style=\"list-style-type: none;\"><strong>Decorating<\/strong> Denise wants to install a square accent of designer tiles in her new shower. She can afford to buy 625 square centimeters of the designer tiles. How long can a side of the accent be?<\/li>\r\n \t<li style=\"list-style-type: none;\"><strong>Decorating<\/strong> Morris wants to have a square mosaic inlaid in his new patio. His budget allows for 2,025 tiles. Each tile is square with an area of one square inch. How long can a side of the mosaic be?\r\n[reveal-answer q=\"898070\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"898070\"]45 inches[\/hidden-answer]<\/li>\r\n<\/ol>\r\n<\/div>\r\n<h3><\/h3>\r\n<div class=\"textbox learning-objectives\">\r\n<h3>Writing exercises<\/h3>\r\n<ul>\r\n \t<li>Why is there no real number equal to [latex]\\sqrt{-64}[\/latex]?<\/li>\r\n \t<li>What is the difference between 9<sup>2<\/sup> and [latex]\\sqrt{9}[\/latex]?[reveal-answer q=\"763299\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"763299\"]Answers will vary. 92 reads: \"nine squared\" and means nine times itself. The expression [latex]\\sqrt{9}[\/latex] reads: \"the square root of nine\" which gives us the number such that if it were multiplied by itself would give you the number inside of the square root.[\/hidden-answer]<\/li>\r\n<\/ul>\r\n<\/div>\r\n&nbsp;<\/li>\r\n<\/ol>","rendered":"<p><strong>Simplify Expressions with Square Roots<\/strong><\/p>\n<p>In the following exercises, simplify.<\/p>\n<ol>\n<li style=\"list-style-type: none;\">\n<ol>\n<li>[latex]\\sqrt{36}[\/latex]\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q401551\">Show Solution<\/span><\/p>\n<div id=\"q401551\" class=\"hidden-answer\" style=\"display: none\">6<\/div>\n<\/div>\n<\/li>\n<li>[latex]\\sqrt{4}[\/latex]<\/li>\n<li>[latex]\\sqrt{64}[\/latex]\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q157868\">Show Solution<\/span><\/p>\n<div id=\"q157868\" class=\"hidden-answer\" style=\"display: none\">8<\/div>\n<\/div>\n<\/li>\n<li>[latex]\\sqrt{144}[\/latex]<\/li>\n<li>[latex]-\\sqrt{4}[\/latex]\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q607127\">Show Solution<\/span><\/p>\n<div id=\"q607127\" class=\"hidden-answer\" style=\"display: none\">\u22122<\/div>\n<\/div>\n<\/li>\n<li>[latex]-\\sqrt{100}[\/latex]<\/li>\n<li>[latex]-\\sqrt{1}[\/latex]\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q273460\">Show Solution<\/span><\/p>\n<div id=\"q273460\" class=\"hidden-answer\" style=\"display: none\">\u22121<\/div>\n<\/div>\n<\/li>\n<li>[latex]-\\sqrt{121}[\/latex]<\/li>\n<li>[latex]\\sqrt{-121}[\/latex]\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q141775\">Show Solution<\/span><\/p>\n<div id=\"q141775\" class=\"hidden-answer\" style=\"display: none\">not a real number<\/div>\n<\/div>\n<\/li>\n<li>[latex]\\sqrt{-36}[\/latex]<\/li>\n<li>[latex]\\sqrt{-9}[\/latex]\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q227141\">Show Solution<\/span><\/p>\n<div id=\"q227141\" class=\"hidden-answer\" style=\"display: none\">not a real number<\/div>\n<\/div>\n<\/li>\n<li>[latex]\\sqrt{-49}[\/latex]<\/li>\n<li>[latex]\\sqrt{9+16}[\/latex]\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q177779\">Show Solution<\/span><\/p>\n<div id=\"q177779\" class=\"hidden-answer\" style=\"display: none\">5<\/div>\n<\/div>\n<\/li>\n<li>[latex]\\sqrt{25+144}[\/latex]<\/li>\n<li>[latex]\\sqrt{9}+\\sqrt{16}[\/latex]\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q652944\">Show Solution<\/span><\/p>\n<div id=\"q652944\" class=\"hidden-answer\" style=\"display: none\">7<\/div>\n<\/div>\n<\/li>\n<li>[latex]\\sqrt{25}+\\sqrt{144}[\/latex]<\/li>\n<li>[latex]\\sqrt{64}[\/latex]<\/li>\n<li>[latex]\\sqrt{144}[\/latex]\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q963585\">Show Solution<\/span><\/p>\n<div id=\"q963585\" class=\"hidden-answer\" style=\"display: none\">12<\/div>\n<\/div>\n<\/li>\n<li>[latex]-\\sqrt{25}[\/latex]<\/li>\n<li>[latex]-\\sqrt{81}[\/latex]\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q189244\">Show Solution<\/span><\/p>\n<div id=\"q189244\" class=\"hidden-answer\" style=\"display: none\">\u22129<\/div>\n<\/div>\n<\/li>\n<li>[latex]\\sqrt{-9}[\/latex]<\/li>\n<li>[latex]\\sqrt{-36}[\/latex]\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q234775\">Show Solution<\/span><\/p>\n<div id=\"q234775\" class=\"hidden-answer\" style=\"display: none\">not a real number<\/div>\n<\/div>\n<\/li>\n<li>[latex]\\sqrt{64}+\\sqrt{225}[\/latex]<\/li>\n<li>[latex]\\sqrt{64+225}[\/latex]\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q766462\">Show Solution<\/span><\/p>\n<div id=\"q766462\" class=\"hidden-answer\" style=\"display: none\">17<\/div>\n<\/div>\n<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<h3><strong>Estimate Square Roots<\/strong><\/h3>\n<p>In the following exercises, estimate each square root between two consecutive whole numbers.<\/p>\n<ol>\n<li style=\"list-style-type: none;\">\n<ol>\n<li>[latex]\\sqrt{70}[\/latex]\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q294230\">Show Solution<\/span><\/p>\n<div id=\"q294230\" class=\"hidden-answer\" style=\"display: none\">[latex]8<\\sqrt{70}<9[\/latex]<\/div>\n<\/div>\n<\/li>\n<li>[latex]\\sqrt{55}[\/latex]<\/li>\n<li>[latex]\\sqrt{200}[\/latex]\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q159114\">Show Solution<\/span><\/p>\n<div id=\"q159114\" class=\"hidden-answer\" style=\"display: none\">[latex]14<\\sqrt{200}<15[\/latex]<\/div>\n<\/div>\n<\/li>\n<li>[latex]\\sqrt{172}[\/latex]<\/li>\n<li>[latex]\\sqrt{28}[\/latex]<\/li>\n<li>[latex]\\sqrt{155}[\/latex]\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q454994\">Show Solution<\/span><\/p>\n<div id=\"q454994\" class=\"hidden-answer\" style=\"display: none\">[latex]12<\\sqrt{155}<13[\/latex]<\/div>\n<\/div>\n<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<h3><strong>Approximate Square Roots with a Calculator<\/strong><\/h3>\n<p>In the following exercises, use a calculator to approximate each square root and round to two decimal places.<\/p>\n<ol>\n<li style=\"list-style-type: none;\">\n<ol>\n<li>[latex]\\sqrt{19}[\/latex]\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q35646\">Show Solution<\/span><\/p>\n<div id=\"q35646\" class=\"hidden-answer\" style=\"display: none\">4.36<\/div>\n<\/div>\n<\/li>\n<li>[latex]\\sqrt{21}[\/latex]<\/li>\n<li>[latex]\\sqrt{53}[\/latex]\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q758190\">Show Solution<\/span><\/p>\n<div id=\"q758190\" class=\"hidden-answer\" style=\"display: none\">7.28<\/div>\n<\/div>\n<\/li>\n<li>[latex]\\sqrt{47}[\/latex]<\/li>\n<li>[latex]\\sqrt{15}[\/latex]<\/li>\n<li>[latex]\\sqrt{57}[\/latex]\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q266393\">Show Solution<\/span><\/p>\n<div id=\"q266393\" class=\"hidden-answer\" style=\"display: none\">7.55<\/div>\n<\/div>\n<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<h3><strong>Simplify Variable Expressions with Square Roots<\/strong><\/h3>\n<p>In the following exercises, simplify. (Assume all variables are greater than or equal to zero.)<\/p>\n<ol>\n<li style=\"list-style-type: none;\">\n<ol>\n<li>[latex]\\sqrt{{y}^{2}}[\/latex]\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q695747\">Show Solution<\/span><\/p>\n<div id=\"q695747\" class=\"hidden-answer\" style=\"display: none\">y<\/div>\n<\/div>\n<\/li>\n<li>[latex]\\sqrt{{b}^{2}}[\/latex]<\/li>\n<li>[latex]\\sqrt{49{x}^{2}}[\/latex]\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q958230\">Show Solution<\/span><\/p>\n<div id=\"q958230\" class=\"hidden-answer\" style=\"display: none\">7x<\/div>\n<\/div>\n<\/li>\n<li>[latex]\\sqrt{100{y}^{2}}[\/latex]<\/li>\n<li>[latex]-\\sqrt{64{a}^{2}}[\/latex]\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q91775\">Show Solution<\/span><\/p>\n<div id=\"q91775\" class=\"hidden-answer\" style=\"display: none\">\u22128a<\/div>\n<\/div>\n<\/li>\n<li>[latex]-\\sqrt{25{x}^{2}}[\/latex]<\/li>\n<li>[latex]\\sqrt{144{x}^{2}{y}^{2}}[\/latex]\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q299115\">Show Solution<\/span><\/p>\n<div id=\"q299115\" class=\"hidden-answer\" style=\"display: none\">12xy<\/div>\n<\/div>\n<\/li>\n<li>[latex]\\sqrt{196{a}^{2}{b}^{2}}[\/latex]<\/li>\n<li>[latex]\\sqrt{{q}^{2}}[\/latex]<\/li>\n<li>[latex]\\sqrt{64{b}^{2}}[\/latex]\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q503702\">Show Solution<\/span><\/p>\n<div id=\"q503702\" class=\"hidden-answer\" style=\"display: none\">8b<\/div>\n<\/div>\n<\/li>\n<li>[latex]-\\sqrt{121{a}^{2}}[\/latex]<\/li>\n<li>[latex]\\sqrt{225{m}^{2}{n}^{2}}[\/latex]\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q646234\">Show Solution<\/span><\/p>\n<div id=\"q646234\" class=\"hidden-answer\" style=\"display: none\">15mn<\/div>\n<\/div>\n<\/li>\n<li>[latex]-\\sqrt{100{q}^{2}}[\/latex]<\/li>\n<li>[latex]\\sqrt{49{y}^{2}}[\/latex]\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q419424\">Show Solution<\/span><\/p>\n<div id=\"q419424\" class=\"hidden-answer\" style=\"display: none\">7y<\/div>\n<\/div>\n<\/li>\n<li>[latex]\\sqrt{4{a}^{2}{b}^{2}}[\/latex]<\/li>\n<li>[latex]\\sqrt{121{c}^{2}{d}^{2}}[\/latex]\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q929578\">Show Solution<\/span><\/p>\n<div id=\"q929578\" class=\"hidden-answer\" style=\"display: none\">11cd<\/div>\n<\/div>\n<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<h3><strong>Use Square Roots in Applications<\/strong><\/h3>\n<p>In the following exercises, solve. Round to one decimal place.<\/p>\n<p><strong>Landscaping<\/strong> Reed wants to have a square garden plot in his backyard. He has enough compost to cover an area of [latex]75[\/latex] square feet. How long can a side of his garden be?<\/p>\n<ol>\n<li style=\"list-style-type: none;\">\n<ol>  <\/ol>\n<\/li>\n<\/ol>\n<ol>\n<li style=\"list-style-type: none;\">\n<ol>  <\/ol>\n<\/li>\n<\/ol>\n<p><strong>Landscaping<\/strong> Vince wants to make a square patio in his yard. He has enough concrete to pave an area of 130 square feet. How long can a side of his patio be?<\/p>\n<p><strong>Gravity<\/strong> An airplane dropped a flare from a height of 1,024 feet above a lake. How many seconds did it take for the flare to reach the water?<\/p>\n<ol>\n<li style=\"list-style-type: none;\">\n<ol>  <\/ol>\n<\/li>\n<\/ol>\n<ol>\n<li style=\"list-style-type: none;\">\n<ol>  <\/ol>\n<\/li>\n<\/ol>\n<p><strong>Gravity <\/strong>A hiker dropped a granola bar from a lookout spot 576 feet above a valley. How long did it take the granola bar to reach the valley floor?<\/p>\n<p><strong>Gravity<\/strong> A hang glider dropped his cell phone from a height of 350 feet. How many seconds did it take for the cell phone to reach the ground?<\/p>\n<p><strong>Gravity<\/strong> A construction worker dropped a hammer while building the Grand Canyon skywalk, 4,000 feet above the Colorado River. How many seconds did it take for the hammer to reach the river?<\/p>\n<ol>\n<li style=\"list-style-type: none;\">\n<ol>  <\/ol>\n<\/li>\n<\/ol>\n<ol>\n<li style=\"list-style-type: none;\">\n<ol>  <\/ol>\n<\/li>\n<\/ol>\n<p><strong>Accident investigation<\/strong> The skid marks from a car involved in an accident measured 54 feet. What was the speed of the car before the brakes were applied?<\/p>\n<p><strong>Accident investigation<\/strong> The skid marks from a car involved in an accident measured 216 feet. What was the speed of the car before the brakes were applied?<\/p>\n<ol>\n<li style=\"list-style-type: none;\">\n<ol>  <\/ol>\n<ol>  <\/ol>\n<\/li>\n<\/ol>\n<p><strong>Accident investigation<\/strong> An accident investigator measured the skid marks of one of the vehicles involved in an accident. The length of the skid marks was 175 feet. What was the speed of the vehicle before the brakes were applied?<\/p>\n<p><strong>Accident investigation<\/strong> An accident investigator measured the skid marks of one of the vehicles involved in an accident. The length of the skid marks was 117 feet. What was the speed of the vehicle before the brakes were applied?<\/p>\n<ol>\n<li style=\"list-style-type: none;\">\n<ol>  <\/ol>\n<ol>  <\/ol>\n<\/li>\n<li style=\"list-style-type: none;\">\n<div class=\"textbox exercises\">\n<h3>Everyday Math<\/h3>\n<ol>\n<li style=\"list-style-type: none;\"><strong>Decorating<\/strong> Denise wants to install a square accent of designer tiles in her new shower. She can afford to buy 625 square centimeters of the designer tiles. How long can a side of the accent be?<\/li>\n<li style=\"list-style-type: none;\"><strong>Decorating<\/strong> Morris wants to have a square mosaic inlaid in his new patio. His budget allows for 2,025 tiles. Each tile is square with an area of one square inch. How long can a side of the mosaic be?\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q898070\">Show Solution<\/span><\/p>\n<div id=\"q898070\" class=\"hidden-answer\" style=\"display: none\">45 inches<\/div>\n<\/div>\n<\/li>\n<\/ol>\n<\/div>\n<h3><\/h3>\n<div class=\"textbox learning-objectives\">\n<h3>Writing exercises<\/h3>\n<ul>\n<li>Why is there no real number equal to [latex]\\sqrt{-64}[\/latex]?<\/li>\n<li>What is the difference between 9<sup>2<\/sup> and [latex]\\sqrt{9}[\/latex]?\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q763299\">Show Answer<\/span><\/p>\n<div id=\"q763299\" class=\"hidden-answer\" style=\"display: none\">Answers will vary. 92 reads: &#8220;nine squared&#8221; and means nine times itself. The expression [latex]\\sqrt{9}[\/latex] reads: &#8220;the square root of nine&#8221; which gives us the number such that if it were multiplied by itself would give you the number inside of the square root.<\/div>\n<\/div>\n<\/li>\n<\/ul>\n<\/div>\n<p>&nbsp;<\/li>\n<\/ol>\n","protected":false},"author":473810,"menu_order":11,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-15613","chapter","type-chapter","status-publish","hentry"],"part":15430,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapters\/15613","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/wp\/v2\/users\/473810"}],"version-history":[{"count":5,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapters\/15613\/revisions"}],"predecessor-version":[{"id":16736,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapters\/15613\/revisions\/16736"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/parts\/15430"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapters\/15613\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/wp\/v2\/media?parent=15613"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapter-type?post=15613"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/wp\/v2\/contributor?post=15613"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/wp\/v2\/license?post=15613"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}