{"id":3084,"date":"2016-07-25T20:12:00","date_gmt":"2016-07-25T20:12:00","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/?post_type=chapter&p=3084"},"modified":"2019-05-04T19:38:28","modified_gmt":"2019-05-04T19:38:28","slug":"putting-it-together-roots-and-rational-exponents","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/chapter\/putting-it-together-roots-and-rational-exponents\/","title":{"raw":"Putting it Together: Roots and Rational Exponents","rendered":"Putting it Together: Roots and Rational Exponents"},"content":{"raw":"[caption id=\"attachment_4000\" align=\"alignright\" width=\"223\"]\"Side Cat heaven[\/caption]\r\n\r\nAt the beginning of this lesson, we left Joan and her brother who were planning to make a ramp for Joan's cat Hobbes from her window. She used the Pythagorean Theorem to get this far, but was left with an equation she did not know how to solve:\r\n

[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>\r\n

The goal was\u00a0to find the unknown length in the following triangle, where c represents the length of the cat ladder.<\/p>\r\n

\"A<\/p>\r\n

Joan's brother, Jacob, suggested that she use a square root to find the solution to her equation. Joan remembered that roots and exponents are related - one \"undoes\" the other. She tried it out in the following way:<\/p>\r\n

[latex]\\begin{array}{ccc}169 ={c}^{2}\\\\\\sqrt{169}=\\sqrt{c^2}\\\\13=c\\end{array}[\/latex]<\/p>\r\n

Hooray! Joan has the length she needs to create her cat's ladder. Hopefully\u00a0she will be able to get some sleep now.<\/p>","rendered":"

\"Side<\/p>\n

Cat heaven<\/p>\n<\/div>\n

At the beginning of this lesson, we left Joan and her brother who were planning to make a ramp for Joan’s cat Hobbes from her window. She used the Pythagorean Theorem to get this far, but was left with an equation she did not know how to solve:<\/p>\n

[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

The goal was\u00a0to find the unknown length in the following triangle, where c represents the length of the cat ladder.<\/p>\n

\"A<\/p>\n

Joan’s brother, Jacob, suggested that she use a square root to find the solution to her equation. Joan remembered that roots and exponents are related – one “undoes” the other. She tried it out in the following way:<\/p>\n

[latex]\\begin{array}{ccc}169 ={c}^{2}\\\\\\sqrt{169}=\\sqrt{c^2}\\\\13=c\\end{array}[\/latex]<\/p>\n

Hooray! Joan has the length she needs to create her cat’s ladder. Hopefully\u00a0she will be able to get some sleep now.<\/p>\n","protected":false},"author":21,"menu_order":14,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"ddf9a735-cadb-453a-ad13-1f4170041945","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-3084","chapter","type-chapter","status-publish","hentry"],"part":893,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/pressbooks\/v2\/chapters\/3084","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/wp\/v2\/users\/21"}],"version-history":[{"count":8,"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/pressbooks\/v2\/chapters\/3084\/revisions"}],"predecessor-version":[{"id":5162,"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/pressbooks\/v2\/chapters\/3084\/revisions\/5162"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/pressbooks\/v2\/parts\/893"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/pressbooks\/v2\/chapters\/3084\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/wp\/v2\/media?parent=3084"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=3084"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/wp\/v2\/contributor?post=3084"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/wp-json\/wp\/v2\/license?post=3084"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}