{"id":279,"date":"2015-09-18T20:30:56","date_gmt":"2015-09-18T20:30:56","guid":{"rendered":"https:\/\/courses.candelalearning.com\/collegealgebra1xmaster\/?post_type=chapter&p=279"},"modified":"2015-11-03T19:20:47","modified_gmt":"2015-11-03T19:20:47","slug":"solutions-3","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/chapter\/solutions-3\/","title":{"raw":"Solutions","rendered":"Solutions"},"content":{"raw":"

Solutions to Try Its<\/h2>\r\n1.\u00a0a. [latex]15[\/latex]\r\nb. [latex]3[\/latex]\r\nc. [latex]4[\/latex]\r\nd. [latex]17[\/latex]\r\n\r\n2.\u00a0[latex]5|x||y|\\sqrt{2yz}[\/latex]. Notice the absolute value signs around x<\/em> and y<\/em>? That\u2019s because their value must be positive!\r\n\r\n3.\u00a0[latex]10|x|[\/latex]\r\n\r\n4.\u00a0[latex]\\frac{x\\sqrt{2}}{3{y}^{2}}[\/latex]. We do not need the absolute value signs for [latex]{y}^{2}[\/latex] because that term will always be nonnegative.\r\n\r\n5.\u00a0[latex]{b}^{4}\\sqrt{3ab}[\/latex]\r\n\r\n6.\u00a0[latex]13\\sqrt{5}[\/latex]\r\n\r\n7.\u00a0[latex]0[\/latex]\r\n\r\n8.\u00a0[latex]6\\sqrt{6}[\/latex]\r\n\r\n9.\u00a0[latex]14 - 7\\sqrt{3}[\/latex]\r\n\r\n10.\u00a0a. [latex]-6[\/latex]\r\nb. [latex]6[\/latex]\r\nc. [latex]88\\sqrt[3]{9}[\/latex]\r\n\r\n11.\u00a0[latex]{\\left(\\sqrt{9}\\right)}^{5}={3}^{5}=243[\/latex]\r\n\r\n12.\u00a0[latex]x{\\left(5y\\right)}^{\\frac{9}{2}}[\/latex]\r\n\r\n13.\u00a0[latex]28{x}^{\\frac{23}{15}}[\/latex]\r\n

Solutions to Odd-Numbered Exercises<\/h2>\r\n1.\u00a0When there is no index, it is assumed to be 2 or the square root. The expression would only be equal to the radicand if the index were 1.\r\n\r\n3.\u00a0The principal square root is the nonnegative root of the number.\r\n\r\n5.\u00a016\r\n\r\n7.\u00a010\r\n\r\n9.\u00a014\r\n\r\n11.\u00a0[latex]7\\sqrt{2}[\/latex]\r\n\r\n13.\u00a0[latex]\\frac{9\\sqrt{5}}{5}[\/latex]\r\n\r\n15.\u00a025\r\n\r\n17.\u00a0[latex]\\sqrt{2}[\/latex]\r\n\r\n19.\u00a0[latex]2\\sqrt{6}[\/latex]\r\n\r\n21.\u00a0[latex]5\\sqrt{6}[\/latex]\r\n\r\n23.\u00a0[latex]6\\sqrt{35}[\/latex]\r\n\r\n25.\u00a0[latex]\\frac{2}{15}[\/latex]\r\n\r\n27.\u00a0[latex]\\frac{6\\sqrt{10}}{19}[\/latex]\r\n\r\n29.\u00a0[latex]-\\frac{1+\\sqrt{17}}{2}[\/latex]\r\n\r\n31.\u00a0[latex]7\\sqrt[3]{2}[\/latex]\r\n\r\n33.\u00a0[latex]15\\sqrt{5}[\/latex]\r\n\r\n35.\u00a0[latex]20{x}^{2}[\/latex]\r\n\r\n37.\u00a0[latex]7\\sqrt{p}[\/latex]\r\n\r\n39.\u00a0[latex]18{m}^{2}\\sqrt{m}[\/latex]\r\n\r\n41.\u00a0[latex]2b\\sqrt{a}[\/latex]\r\n\r\n43.\u00a0[latex]\\frac{15x}{7}[\/latex]\r\n\r\n45.\u00a0[latex]5{y}^{4}\\sqrt{2}[\/latex]\r\n\r\n47.\u00a0[latex]\\frac{4\\sqrt{7d}}{7d}[\/latex]\r\n\r\n49.\u00a0[latex]\\frac{2\\sqrt{2}+2\\sqrt{6x}}{1 - 3x}[\/latex]\r\n\r\n51.\u00a0[latex]-w\\sqrt{2w}[\/latex]\r\n\r\n53.\u00a0[latex]\\frac{3\\sqrt{x}-\\sqrt{3x}}{2}[\/latex]\r\n\r\n55.\u00a0[latex]5{n}^{5}\\sqrt{5}[\/latex]\r\n\r\n57.\u00a0[latex]\\frac{9\\sqrt{m}}{19m}[\/latex]\r\n\r\n59.\u00a0[latex]\\frac{2}{3d}[\/latex]\r\n\r\n61.\u00a0[latex]\\frac{3\\sqrt[4]{2{x}^{2}}}{2}[\/latex]\r\n\r\n63.\u00a0[latex]6z\\sqrt[3]{2}[\/latex]\r\n\r\n65.\u00a0500 feet\r\n\r\n67.\u00a0[latex]\\frac{-5\\sqrt{2}-6}{7}[\/latex]\r\n\r\n69.\u00a0[latex]\\frac{\\sqrt{mnc}}{{a}^{9}cmn}[\/latex]\r\n\r\n71.\u00a0[latex]\\frac{2\\sqrt{2}x+\\sqrt{2}}{4}[\/latex]\r\n\r\n73.\u00a0[latex]\\frac{\\sqrt{3}}{3}[\/latex]","rendered":"

Solutions to Try Its<\/h2>\n

1.\u00a0a. [latex]15[\/latex]
\nb. [latex]3[\/latex]
\nc. [latex]4[\/latex]
\nd. [latex]17[\/latex]<\/p>\n

2.\u00a0[latex]5|x||y|\\sqrt{2yz}[\/latex]. Notice the absolute value signs around x<\/em> and y<\/em>? That\u2019s because their value must be positive!<\/p>\n

3.\u00a0[latex]10|x|[\/latex]<\/p>\n

4.\u00a0[latex]\\frac{x\\sqrt{2}}{3{y}^{2}}[\/latex]. We do not need the absolute value signs for [latex]{y}^{2}[\/latex] because that term will always be nonnegative.<\/p>\n

5.\u00a0[latex]{b}^{4}\\sqrt{3ab}[\/latex]<\/p>\n

6.\u00a0[latex]13\\sqrt{5}[\/latex]<\/p>\n

7.\u00a0[latex]0[\/latex]<\/p>\n

8.\u00a0[latex]6\\sqrt{6}[\/latex]<\/p>\n

9.\u00a0[latex]14 - 7\\sqrt{3}[\/latex]<\/p>\n

10.\u00a0a. [latex]-6[\/latex]
\nb. [latex]6[\/latex]
\nc. [latex]88\\sqrt[3]{9}[\/latex]<\/p>\n

11.\u00a0[latex]{\\left(\\sqrt{9}\\right)}^{5}={3}^{5}=243[\/latex]<\/p>\n

12.\u00a0[latex]x{\\left(5y\\right)}^{\\frac{9}{2}}[\/latex]<\/p>\n

13.\u00a0[latex]28{x}^{\\frac{23}{15}}[\/latex]<\/p>\n

Solutions to Odd-Numbered Exercises<\/h2>\n

1.\u00a0When there is no index, it is assumed to be 2 or the square root. The expression would only be equal to the radicand if the index were 1.<\/p>\n

3.\u00a0The principal square root is the nonnegative root of the number.<\/p>\n

5.\u00a016<\/p>\n

7.\u00a010<\/p>\n

9.\u00a014<\/p>\n

11.\u00a0[latex]7\\sqrt{2}[\/latex]<\/p>\n

13.\u00a0[latex]\\frac{9\\sqrt{5}}{5}[\/latex]<\/p>\n

15.\u00a025<\/p>\n

17.\u00a0[latex]\\sqrt{2}[\/latex]<\/p>\n

19.\u00a0[latex]2\\sqrt{6}[\/latex]<\/p>\n

21.\u00a0[latex]5\\sqrt{6}[\/latex]<\/p>\n

23.\u00a0[latex]6\\sqrt{35}[\/latex]<\/p>\n

25.\u00a0[latex]\\frac{2}{15}[\/latex]<\/p>\n

27.\u00a0[latex]\\frac{6\\sqrt{10}}{19}[\/latex]<\/p>\n

29.\u00a0[latex]-\\frac{1+\\sqrt{17}}{2}[\/latex]<\/p>\n

31.\u00a0[latex]7\\sqrt[3]{2}[\/latex]<\/p>\n

33.\u00a0[latex]15\\sqrt{5}[\/latex]<\/p>\n

35.\u00a0[latex]20{x}^{2}[\/latex]<\/p>\n

37.\u00a0[latex]7\\sqrt{p}[\/latex]<\/p>\n

39.\u00a0[latex]18{m}^{2}\\sqrt{m}[\/latex]<\/p>\n

41.\u00a0[latex]2b\\sqrt{a}[\/latex]<\/p>\n

43.\u00a0[latex]\\frac{15x}{7}[\/latex]<\/p>\n

45.\u00a0[latex]5{y}^{4}\\sqrt{2}[\/latex]<\/p>\n

47.\u00a0[latex]\\frac{4\\sqrt{7d}}{7d}[\/latex]<\/p>\n

49.\u00a0[latex]\\frac{2\\sqrt{2}+2\\sqrt{6x}}{1 - 3x}[\/latex]<\/p>\n

51.\u00a0[latex]-w\\sqrt{2w}[\/latex]<\/p>\n

53.\u00a0[latex]\\frac{3\\sqrt{x}-\\sqrt{3x}}{2}[\/latex]<\/p>\n

55.\u00a0[latex]5{n}^{5}\\sqrt{5}[\/latex]<\/p>\n

57.\u00a0[latex]\\frac{9\\sqrt{m}}{19m}[\/latex]<\/p>\n

59.\u00a0[latex]\\frac{2}{3d}[\/latex]<\/p>\n

61.\u00a0[latex]\\frac{3\\sqrt[4]{2{x}^{2}}}{2}[\/latex]<\/p>\n

63.\u00a0[latex]6z\\sqrt[3]{2}[\/latex]<\/p>\n

65.\u00a0500 feet<\/p>\n

67.\u00a0[latex]\\frac{-5\\sqrt{2}-6}{7}[\/latex]<\/p>\n

69.\u00a0[latex]\\frac{\\sqrt{mnc}}{{a}^{9}cmn}[\/latex]<\/p>\n

71.\u00a0[latex]\\frac{2\\sqrt{2}x+\\sqrt{2}}{4}[\/latex]<\/p>\n

73.\u00a0[latex]\\frac{\\sqrt{3}}{3}[\/latex]<\/p>\n\n\t\t\t

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Candela Citations<\/h3>\n\t\t\t\t\t
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