{"id":4463,"date":"2016-10-03T21:26:15","date_gmt":"2016-10-03T21:26:15","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/?post_type=chapter&#038;p=4463"},"modified":"2017-07-27T17:14:19","modified_gmt":"2017-07-27T17:14:19","slug":"conclusion-12","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/tallahassee-intermediatealgebra\/chapter\/conclusion-12\/","title":{"raw":"Putting It Together: Roots and Rational Exponents","rendered":"Putting It Together: Roots and Rational Exponents"},"content":{"raw":"<img class=\"size-medium wp-image-4000 alignleft\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/121\/2016\/08\/17161656\/Screen-Shot-2016-08-17-at-9.16.31-AM-223x300.png\" alt=\"Side of apartment building with 6 section cat ladder attached to the side leading to an apartment balcony\" width=\"223\" height=\"300\" \/>At the beginning of this lesson, we left Joan and her sister as they were planning to make a ramp for Joan's cat Hobbes from her window. \u00a0She used the Pythagorean Theorem to get this far, but was left with an equation she didn't know how to solve:\r\n\r\n[latex]\\begin{array}{ccc}\\hfill {a}^{2}+{b}^{2}&amp; =&amp; {c}^{2}\\hfill \\\\ \\hfill {5}^{2}+{12}^{2}&amp; =&amp; {c}^{2}\\hfill \\\\ \\hfill 169&amp; =&amp; {c}^{2}\\hfill \\end{array}[\/latex]\r\n\r\nThe goal was\u00a0to find the unknown length in the following triangle, where c represents the length of the cat ladder.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/924\/2015\/09\/25200219\/CNX_CAT_Figure_01_03_001.jpg\" alt=\"A right triangle with a base of 5 feet, a height of 12 feet, and a hypotenuse labeled c\" width=\"487\" height=\"284\" \/>\r\n\r\nJoan's sister, Anne, suggested that she use a square root to find the solution to her equation. \u00a0Joan remembered that roots and exponents are related - one \"undoes\" the other. She tried it out in the following way:\r\n\r\n[latex]\\begin{array}{ccc}169 ={c}^{2}\\\\\\sqrt{169}=\\sqrt{c^2}\\\\13=c\\end{array}[\/latex]\r\n\r\nHooray! \u00a0Joan has the length she needs to create her cat's ladder. Hopefully\u00a0she will be able to get some sleep now.","rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-4000 alignleft\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/121\/2016\/08\/17161656\/Screen-Shot-2016-08-17-at-9.16.31-AM-223x300.png\" alt=\"Side of apartment building with 6 section cat ladder attached to the side leading to an apartment balcony\" width=\"223\" height=\"300\" \/>At the beginning of this lesson, we left Joan and her sister as they were planning to make a ramp for Joan&#8217;s cat Hobbes from her window. \u00a0She used the Pythagorean Theorem to get this far, but was left with an equation she didn&#8217;t know how to solve:<\/p>\n<p>[latex]\\begin{array}{ccc}\\hfill {a}^{2}+{b}^{2}& =& {c}^{2}\\hfill \\\\ \\hfill {5}^{2}+{12}^{2}& =& {c}^{2}\\hfill \\\\ \\hfill 169& =& {c}^{2}\\hfill \\end{array}[\/latex]<\/p>\n<p>The goal was\u00a0to find the unknown length in the following triangle, where c represents the length of the cat ladder.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/924\/2015\/09\/25200219\/CNX_CAT_Figure_01_03_001.jpg\" alt=\"A right triangle with a base of 5 feet, a height of 12 feet, and a hypotenuse labeled c\" width=\"487\" height=\"284\" \/><\/p>\n<p>Joan&#8217;s sister, Anne, suggested that she use a square root to find the solution to her equation. \u00a0Joan remembered that roots and exponents are related &#8211; one &#8220;undoes&#8221; the other. She tried it out in the following way:<\/p>\n<p>[latex]\\begin{array}{ccc}169 ={c}^{2}\\\\\\sqrt{169}=\\sqrt{c^2}\\\\13=c\\end{array}[\/latex]<\/p>\n<p>Hooray! \u00a0Joan has the length she needs to create her cat&#8217;s ladder. Hopefully\u00a0she will be able to get some sleep now.<\/p>\n","protected":false},"author":21,"menu_order":5,"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-4463","chapter","type-chapter","status-publish","hentry"],"part":893,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/tallahassee-intermediatealgebra\/wp-json\/pressbooks\/v2\/chapters\/4463","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/tallahassee-intermediatealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/tallahassee-intermediatealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/tallahassee-intermediatealgebra\/wp-json\/wp\/v2\/users\/21"}],"version-history":[{"count":2,"href":"https:\/\/courses.lumenlearning.com\/tallahassee-intermediatealgebra\/wp-json\/pressbooks\/v2\/chapters\/4463\/revisions"}],"predecessor-version":[{"id":4556,"href":"https:\/\/courses.lumenlearning.com\/tallahassee-intermediatealgebra\/wp-json\/pressbooks\/v2\/chapters\/4463\/revisions\/4556"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/tallahassee-intermediatealgebra\/wp-json\/pressbooks\/v2\/parts\/893"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/tallahassee-intermediatealgebra\/wp-json\/pressbooks\/v2\/chapters\/4463\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/tallahassee-intermediatealgebra\/wp-json\/wp\/v2\/media?parent=4463"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/tallahassee-intermediatealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=4463"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/tallahassee-intermediatealgebra\/wp-json\/wp\/v2\/contributor?post=4463"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/tallahassee-intermediatealgebra\/wp-json\/wp\/v2\/license?post=4463"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}