{"id":10406,"date":"2017-05-26T19:00:01","date_gmt":"2017-05-26T19:00:01","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=10406"},"modified":"2020-02-02T04:11:43","modified_gmt":"2020-02-02T04:11:43","slug":"using-square-roots-in-applications","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/chapter\/using-square-roots-in-applications\/","title":{"raw":"Using Square Roots in Applications","rendered":"Using Square Roots in Applications"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Solve application problems that include the use of square roots<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2>Use Square Roots in Applications<\/h2>\r\nAs you progress through your college courses, you\u2019ll encounter several applications of square roots. Once again, if we use our strategy for applications, it will give us a plan for finding the answer!\r\n<div class=\"textbox shaded\">\r\n<h3>Use a strategy for applications with square roots.<\/h3>\r\n<ol id=\"eip-id1168466250274\" class=\"stepwise\">\r\n \t<li>Identify what you are asked to find.<\/li>\r\n \t<li>Write a phrase that gives the information to find it.<\/li>\r\n \t<li>Translate the phrase to an expression.<\/li>\r\n \t<li>Simplify the expression.<\/li>\r\n \t<li>Write a complete sentence that answers the question.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<h2>Square Roots and Area<\/h2>\r\nWe have solved applications with area before. If we were given the length of the sides of a square, we could find its area by squaring the length of its sides. Now we can find the length of the sides of a square if we are given the area, by finding the square root of the area.\r\nIf the area of the square is [latex]A[\/latex] square units, the length of a side is [latex]\\sqrt{A}[\/latex] units. See\u00a0the table below.\r\n<table id=\"fs-id1973397\" summary=\"A table is shown with 2 columns and 4 rows. The first column is labeled \">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th>Area (square units)<\/th>\r\n<th>Length of side (units)<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td>[latex]9[\/latex]<\/td>\r\n<td>[latex]\\sqrt{9}=3[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]144[\/latex]<\/td>\r\n<td>[latex]\\sqrt{144}=12[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]A[\/latex]<\/td>\r\n<td>[latex]\\sqrt{A}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nMike and Lychelle want to make a square patio. They have enough concrete for an area of [latex]200[\/latex] square feet. To the nearest tenth of a foot, how long can a side of their square patio be?\r\n\r\nSolution\r\nWe know the area of the square is [latex]200[\/latex] square feet and want to find the length of the side. If the area of the square is [latex]A[\/latex] square units, the length of a side is [latex]\\sqrt{A}[\/latex] units.\r\n<table id=\"eip-id1168468768448\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>What are you asked to find?<\/td>\r\n<td>The length of each side of a square patio<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write a phrase.<\/td>\r\n<td>The length of a side<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Translate to an expression.<\/td>\r\n<td>[latex]\\sqrt{A}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Evaluate [latex]\\sqrt{A}[\/latex] when [latex]A=200[\/latex] .<\/td>\r\n<td>[latex]\\sqrt{200}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Use your calculator.<\/td>\r\n<td>[latex]14.142135..[\/latex].<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Round to one decimal place.<\/td>\r\n<td>[latex]\\text{14.1 feet}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write a sentence.<\/td>\r\n<td>Each side of the patio should be [latex]14.1[\/latex] feet.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146641[\/ohm_question]\r\n\r\n<\/div>\r\n<h2>Square Roots and Gravity<\/h2>\r\nAnother application of square roots involves gravity. On Earth, if an object is dropped from a height of [latex]h[\/latex] feet, the time in seconds it will take to reach the ground is found by evaluating the expression [latex]{\\Large\\frac{\\sqrt{h}}{4}}[\/latex]. For example, if an object is dropped from a height of [latex]64[\/latex] feet, we can find the time it takes to reach the ground by evaluating [latex]{\\Large\\frac{\\sqrt{64}}{4}}[\/latex].\r\n<table id=\"eip-id1168466722027\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]{\\Large\\frac{\\sqrt{64}}{4}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Take the square root of [latex]64[\/latex].<\/td>\r\n<td>[latex]{\\Large\\frac{8}{4}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify the fraction.<\/td>\r\n<td>[latex]2[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nIt would take [latex]2[\/latex] seconds for an object dropped from a height of [latex]64[\/latex] feet to reach the ground.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nChristy dropped her sunglasses from a bridge [latex]400[\/latex] feet above a river. How many seconds does it take for the sunglasses to reach the river?\r\n[reveal-answer q=\"127186\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"127186\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168468767850\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>What are you asked to find?<\/td>\r\n<td>The number of seconds it takes for the sunglasses to reach the river<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write a phrase.<\/td>\r\n<td>The time it will take to reach the river<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Translate to an expression.<\/td>\r\n<td>[latex]{\\Large\\frac{\\sqrt{h}}{4}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Evaluate [latex]\\Large\\frac{\\sqrt{h}}{4}[\/latex] when [latex]h=400[\/latex] .<\/td>\r\n<td>[latex]{\\Large\\frac{\\sqrt{400}}{4}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Find the square root of [latex]400[\/latex].<\/td>\r\n<td>[latex]{\\Large\\frac{20}{4}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]5[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write a sentence.<\/td>\r\n<td>It will take [latex]5[\/latex] seconds for the sunglasses to reach the river.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146642[\/ohm_question]\r\n\r\n[ohm_question]146643[\/ohm_question]\r\n\r\n<\/div>\r\n<h2>Square Roots and Accident Investigations<\/h2>\r\nPolice officers investigating car accidents measure the length of the skid marks on the pavement. Then they use square roots to determine the speed, in miles per hour, a car was going before applying the brakes. According to some formulas, if the length of the skid marks is [latex]d[\/latex] feet, then the speed of the car can be found by evaluating [latex]\\sqrt{24d}[\/latex].\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nAfter a car accident, the skid marks for one car measured [latex]190[\/latex] feet. To the nearest tenth, what was the speed of the car (in mph) before the brakes were applied?\r\n[reveal-answer q=\"838425\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"838425\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168468505344\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>What are you asked to find?<\/td>\r\n<td>The speed of the car before the brakes were applied<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write a phrase.<\/td>\r\n<td>The speed of the car<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Translate to an expression.<\/td>\r\n<td>[latex]\\sqrt{24d}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Evaluate [latex]\\sqrt{24d}[\/latex] when [latex]d=190[\/latex].<\/td>\r\n<td>[latex]\\sqrt{24\\cdot 190}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]\\sqrt{4,560}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Use your calculator.<\/td>\r\n<td>[latex]67.527772..[\/latex].<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Round to tenths.<\/td>\r\n<td>[latex]67.5[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write a sentence.<\/td>\r\n<td>The speed of the car was approximately [latex]67.5[\/latex] miles per hour.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146644[\/ohm_question]\r\n\r\n<\/div>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Solve application problems that include the use of square roots<\/li>\n<\/ul>\n<\/div>\n<h2>Use Square Roots in Applications<\/h2>\n<p>As you progress through your college courses, you\u2019ll encounter several applications of square roots. Once again, if we use our strategy for applications, it will give us a plan for finding the answer!<\/p>\n<div class=\"textbox shaded\">\n<h3>Use a strategy for applications with square roots.<\/h3>\n<ol id=\"eip-id1168466250274\" class=\"stepwise\">\n<li>Identify what you are asked to find.<\/li>\n<li>Write a phrase that gives the information to find it.<\/li>\n<li>Translate the phrase to an expression.<\/li>\n<li>Simplify the expression.<\/li>\n<li>Write a complete sentence that answers the question.<\/li>\n<\/ol>\n<\/div>\n<h2>Square Roots and Area<\/h2>\n<p>We have solved applications with area before. If we were given the length of the sides of a square, we could find its area by squaring the length of its sides. Now we can find the length of the sides of a square if we are given the area, by finding the square root of the area.<br \/>\nIf the area of the square is [latex]A[\/latex] square units, the length of a side is [latex]\\sqrt{A}[\/latex] units. See\u00a0the table below.<\/p>\n<table id=\"fs-id1973397\" summary=\"A table is shown with 2 columns and 4 rows. The first column is labeled\">\n<thead>\n<tr valign=\"top\">\n<th>Area (square units)<\/th>\n<th>Length of side (units)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td>[latex]9[\/latex]<\/td>\n<td>[latex]\\sqrt{9}=3[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]144[\/latex]<\/td>\n<td>[latex]\\sqrt{144}=12[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]A[\/latex]<\/td>\n<td>[latex]\\sqrt{A}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Mike and Lychelle want to make a square patio. They have enough concrete for an area of [latex]200[\/latex] square feet. To the nearest tenth of a foot, how long can a side of their square patio be?<\/p>\n<p>Solution<br \/>\nWe know the area of the square is [latex]200[\/latex] square feet and want to find the length of the side. If the area of the square is [latex]A[\/latex] square units, the length of a side is [latex]\\sqrt{A}[\/latex] units.<\/p>\n<table id=\"eip-id1168468768448\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>What are you asked to find?<\/td>\n<td>The length of each side of a square patio<\/td>\n<\/tr>\n<tr>\n<td>Write a phrase.<\/td>\n<td>The length of a side<\/td>\n<\/tr>\n<tr>\n<td>Translate to an expression.<\/td>\n<td>[latex]\\sqrt{A}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Evaluate [latex]\\sqrt{A}[\/latex] when [latex]A=200[\/latex] .<\/td>\n<td>[latex]\\sqrt{200}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Use your calculator.<\/td>\n<td>[latex]14.142135..[\/latex].<\/td>\n<\/tr>\n<tr>\n<td>Round to one decimal place.<\/td>\n<td>[latex]\\text{14.1 feet}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write a sentence.<\/td>\n<td>Each side of the patio should be [latex]14.1[\/latex] feet.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146641\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146641&theme=oea&iframe_resize_id=ohm146641&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<h2>Square Roots and Gravity<\/h2>\n<p>Another application of square roots involves gravity. On Earth, if an object is dropped from a height of [latex]h[\/latex] feet, the time in seconds it will take to reach the ground is found by evaluating the expression [latex]{\\Large\\frac{\\sqrt{h}}{4}}[\/latex]. For example, if an object is dropped from a height of [latex]64[\/latex] feet, we can find the time it takes to reach the ground by evaluating [latex]{\\Large\\frac{\\sqrt{64}}{4}}[\/latex].<\/p>\n<table id=\"eip-id1168466722027\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]{\\Large\\frac{\\sqrt{64}}{4}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Take the square root of [latex]64[\/latex].<\/td>\n<td>[latex]{\\Large\\frac{8}{4}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify the fraction.<\/td>\n<td>[latex]2[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>It would take [latex]2[\/latex] seconds for an object dropped from a height of [latex]64[\/latex] feet to reach the ground.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Christy dropped her sunglasses from a bridge [latex]400[\/latex] feet above a river. How many seconds does it take for the sunglasses to reach the river?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q127186\">Show Solution<\/span><\/p>\n<div id=\"q127186\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168468767850\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>What are you asked to find?<\/td>\n<td>The number of seconds it takes for the sunglasses to reach the river<\/td>\n<\/tr>\n<tr>\n<td>Write a phrase.<\/td>\n<td>The time it will take to reach the river<\/td>\n<\/tr>\n<tr>\n<td>Translate to an expression.<\/td>\n<td>[latex]{\\Large\\frac{\\sqrt{h}}{4}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Evaluate [latex]\\Large\\frac{\\sqrt{h}}{4}[\/latex] when [latex]h=400[\/latex] .<\/td>\n<td>[latex]{\\Large\\frac{\\sqrt{400}}{4}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Find the square root of [latex]400[\/latex].<\/td>\n<td>[latex]{\\Large\\frac{20}{4}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]5[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write a sentence.<\/td>\n<td>It will take [latex]5[\/latex] seconds for the sunglasses to reach the river.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146642\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146642&theme=oea&iframe_resize_id=ohm146642&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146643\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146643&theme=oea&iframe_resize_id=ohm146643&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<h2>Square Roots and Accident Investigations<\/h2>\n<p>Police officers investigating car accidents measure the length of the skid marks on the pavement. Then they use square roots to determine the speed, in miles per hour, a car was going before applying the brakes. According to some formulas, if the length of the skid marks is [latex]d[\/latex] feet, then the speed of the car can be found by evaluating [latex]\\sqrt{24d}[\/latex].<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>After a car accident, the skid marks for one car measured [latex]190[\/latex] feet. To the nearest tenth, what was the speed of the car (in mph) before the brakes were applied?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q838425\">Show Solution<\/span><\/p>\n<div id=\"q838425\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168468505344\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>What are you asked to find?<\/td>\n<td>The speed of the car before the brakes were applied<\/td>\n<\/tr>\n<tr>\n<td>Write a phrase.<\/td>\n<td>The speed of the car<\/td>\n<\/tr>\n<tr>\n<td>Translate to an expression.<\/td>\n<td>[latex]\\sqrt{24d}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Evaluate [latex]\\sqrt{24d}[\/latex] when [latex]d=190[\/latex].<\/td>\n<td>[latex]\\sqrt{24\\cdot 190}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]\\sqrt{4,560}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Use your calculator.<\/td>\n<td>[latex]67.527772..[\/latex].<\/td>\n<\/tr>\n<tr>\n<td>Round to tenths.<\/td>\n<td>[latex]67.5[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write a sentence.<\/td>\n<td>The speed of the car was approximately [latex]67.5[\/latex] miles per hour.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146644\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146644&theme=oea&iframe_resize_id=ohm146644&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-10406\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Question ID 146644. 146643, 146642, 146641. <strong>Authored by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: IMathAS Community License CC-BY + GPL<\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>Prealgebra. <strong>Provided by<\/strong>: OpenStax. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":17533,"menu_order":15,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757\"},{\"type\":\"original\",\"description\":\"Question ID 146644. 146643, 146642, 146641\",\"author\":\"Lumen Learning\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"IMathAS Community License CC-BY + GPL\"}]","CANDELA_OUTCOMES_GUID":"d794c59b-01fb-4e95-b3cf-86113a87493a","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-10406","chapter","type-chapter","status-publish","hentry"],"part":13985,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/10406","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":18,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/10406\/revisions"}],"predecessor-version":[{"id":15953,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/10406\/revisions\/15953"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/parts\/13985"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/10406\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/wp\/v2\/media?parent=10406"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=10406"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/wp\/v2\/contributor?post=10406"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/wp\/v2\/license?post=10406"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}