{"id":84,"date":"2024-10-16T18:28:53","date_gmt":"2024-10-16T18:28:53","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/?post_type=chapter&#038;p=84"},"modified":"2024-10-16T18:28:53","modified_gmt":"2024-10-16T18:28:53","slug":"radicals-and-rational-exponents-apply-it-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/chapter\/radicals-and-rational-exponents-apply-it-1\/","title":{"raw":"Radicals and Rational Exponents: Apply It 1","rendered":"Radicals and Rational Exponents: Apply It 1"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n \t<li>Calculate square roots and apply them in basic operations like addition, subtraction, and rationalizing the denominators.<\/li>\r\n \t<li>Use the product and quotient rules to simplify expressions that include square roots.<\/li>\r\n \t<li>Understand how to use rational exponents in expressions and recognize their connection to roots for simplifying calculations.<\/li>\r\n<\/ul>\r\n<\/section>Quilt blocks are fabric components sewn together to make a quilt. The quilt block design of a square within a square is called an \u201ceconomy quilt block.\u201d A textile artist is making a quilt using economy quilt blocks of varying sizes, so he makes a sketch of the design with side length `w` as shown below.\r\n\r\n<img class=\"alignnone size-medium wp-image-4198\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/04\/25002727\/quilt_block-300x197.jpg\" alt=\"\" width=\"300\" height=\"197\" \/>\r\n\r\nThe artist needs to calculate how many square inches of fabric he will need for each orange triangle. First, he will need to determine an expression for the hypotenuse.\r\n\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm2_question hide_question_numbers=1]25367[\/ohm2_question]<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm2_question hide_question_numbers=1]25368[\/ohm2_question]<\/section><img class=\"alignnone size-medium wp-image-4199\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/04\/25002849\/triangle-300x204.jpg\" alt=\"\" width=\"300\" height=\"204\" \/>\r\n\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm2_question hide_question_numbers=1]25369[\/ohm2_question]<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm2_question hide_question_numbers=1]25370[\/ohm2_question]<\/section>*It would help to have the measurements labeled in the diagram.\r\n\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm2_question hide_question_numbers=1]25371[\/ohm2_question]<\/section><img class=\"alignnone size-medium wp-image-4200\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/04\/25002953\/real_quilt_block-300x200.jpg\" alt=\"\" width=\"300\" height=\"200\" \/>Photo by <a href=\"https:\/\/unsplash.com\/@ripey__?utm_content=creditCopyText&amp;utm_medium=referral&amp;utm_source=unsplash\">Ibrahim Rifath<\/a> on <a href=\"https:\/\/unsplash.com\/photos\/elephant-print-at-n3k8sCkxpKU?utm_content=creditCopyText&amp;utm_medium=referral&amp;utm_source=unsplash\">Unsplash<\/a>\r\n\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm2_question hide_question_numbers=1]25372[\/ohm2_question]<\/section>&nbsp;","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Calculate square roots and apply them in basic operations like addition, subtraction, and rationalizing the denominators.<\/li>\n<li>Use the product and quotient rules to simplify expressions that include square roots.<\/li>\n<li>Understand how to use rational exponents in expressions and recognize their connection to roots for simplifying calculations.<\/li>\n<\/ul>\n<\/section>\n<p>Quilt blocks are fabric components sewn together to make a quilt. The quilt block design of a square within a square is called an \u201ceconomy quilt block.\u201d A textile artist is making a quilt using economy quilt blocks of varying sizes, so he makes a sketch of the design with side length `w` as shown below.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-4198\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/04\/25002727\/quilt_block-300x197.jpg\" alt=\"\" width=\"300\" height=\"197\" \/><\/p>\n<p>The artist needs to calculate how many square inches of fabric he will need for each orange triangle. First, he will need to determine an expression for the hypotenuse.<\/p>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm25367\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=25367&theme=lumen&iframe_resize_id=ohm25367&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm25368\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=25368&theme=lumen&iframe_resize_id=ohm25368&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-4199\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/04\/25002849\/triangle-300x204.jpg\" alt=\"\" width=\"300\" height=\"204\" \/><\/p>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm25369\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=25369&theme=lumen&iframe_resize_id=ohm25369&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm25370\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=25370&theme=lumen&iframe_resize_id=ohm25370&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p>*It would help to have the measurements labeled in the diagram.<\/p>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm25371\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=25371&theme=lumen&iframe_resize_id=ohm25371&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-4200\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/04\/25002953\/real_quilt_block-300x200.jpg\" alt=\"\" width=\"300\" height=\"200\" \/>Photo by <a href=\"https:\/\/unsplash.com\/@ripey__?utm_content=creditCopyText&amp;utm_medium=referral&amp;utm_source=unsplash\">Ibrahim Rifath<\/a> on <a href=\"https:\/\/unsplash.com\/photos\/elephant-print-at-n3k8sCkxpKU?utm_content=creditCopyText&amp;utm_medium=referral&amp;utm_source=unsplash\">Unsplash<\/a><\/p>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm25372\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=25372&theme=lumen&iframe_resize_id=ohm25372&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p>&nbsp;<\/p>\n","protected":false},"author":15,"menu_order":27,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":28,"module-header":"- Select Header -","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/pressbooks\/v2\/chapters\/84"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/wp\/v2\/users\/15"}],"version-history":[{"count":1,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/pressbooks\/v2\/chapters\/84\/revisions"}],"predecessor-version":[{"id":93,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/pressbooks\/v2\/chapters\/84\/revisions\/93"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/pressbooks\/v2\/parts\/28"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/pressbooks\/v2\/chapters\/84\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/wp\/v2\/media?parent=84"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/pressbooks\/v2\/chapter-type?post=84"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/wp\/v2\/contributor?post=84"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/wp\/v2\/license?post=84"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}