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9.2 Simplify Square Roots

Product and Quotient Properties used to pull perfect-square factors out of a radicand and to reduce the root of a fraction to lowest terms.

Elementary Algebra 2e, 9.2 Simplify Square Roots

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98 exercises

9.2 Exercise 1

Before you get started take this readiness quiz.

Simplify: 80176\frac{80}{176}.
If you missed this problem, review the reference.

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9.2 Exercise 2

Simplify: n9n3\frac{n^{9}}{n^{3}}.
If you missed this problem, review the reference.

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9.2 Exercise 3

Simplify: q4q12\frac{q^{4}}{q^{12}}.
If you missed this problem, review the reference.

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9.2 Exercise 5

Simplify: 48\sqrt{48}.

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9.2 Exercise 6

Simplify: 45\sqrt{45}.

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9.2 Exercise 7

Simplify: 500\sqrt{500}.

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9.2 Exercise 8

Simplify: 288\sqrt{288}.

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9.2 Exercise 9

Simplify: 432\sqrt{432}.

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9.2 Exercise 10

Simplify: x3\sqrt{x^{3}}.

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9.2 Exercise 11

Simplify: b5\sqrt{b^{5}}.

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9.2 Exercise 12

Simplify: p9\sqrt{p^{9}}.

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9.2 Exercise 13

Simplify: 25y5.\sqrt{25 y^{5} .}

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9.2 Exercise 14

Simplify: 16x7\sqrt{16 x^{7}}.

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9.2 Exercise 15

Simplify: 49v9\sqrt{49 v^{9}}.

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9.2 Exercise 16

Simplify: 72n7\sqrt{72 n^{7}}.

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9.2 Exercise 17

Simplify: 32y5\sqrt{32 y^{5}}.

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9.2 Exercise 18

Simplify: 75a9\sqrt{75 a^{9}}.

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9.2 Exercise 19

Simplify: 63u3v5\sqrt{63 u^{3} v^{5}}.

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9.2 Exercise 20

Simplify: 98a7b5\sqrt{98 a^{7} b^{5}}.

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9.2 Exercise 21

Simplify: 180m9n11\sqrt{180 m^{9} n^{11}}.

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9.2 Exercise 22

Simplify: 3+323 + \sqrt{32}.

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9.2 Exercise 23

Simplify: 5+755 + \sqrt{75}.

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9.2 Exercise 24

Simplify: 2+982 + \sqrt{98}.

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9.2 Exercise 25

Simplify: 4−482\frac{4 - \sqrt{48}}{2}.

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9.2 Exercise 26

Simplify: 10−755\frac{10 - \sqrt{75}}{5}.

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9.2 Exercise 27

Simplify: 6−453\frac{6 - \sqrt{45}}{3}.

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9.2 Exercise 28

Simplify: 964\sqrt{\frac{9}{64}}.

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9.2 Exercise 29

Simplify: 2516\sqrt{\frac{25}{16}}.

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9.2 Exercise 30

Simplify: 4981\sqrt{\frac{49}{81}}.

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9.2 Exercise 31

Simplify: 4580\sqrt{\frac{45}{80}}.

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9.2 Exercise 32

Simplify: 7548\sqrt{\frac{75}{48}}.

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9.2 Exercise 33

Simplify: 98162\sqrt{\frac{98}{162}}.

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9.2 Exercise 34

Simplify: m6m4\sqrt{\frac{m^{6}}{m^{4}}}.

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9.2 Exercise 35

Simplify: a8a6\sqrt{\frac{a^{8}}{a^{6}}}.

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9.2 Exercise 36

Simplify: x14x10\sqrt{\frac{x^{14}}{x^{10}}}.

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9.2 Exercise 37

Simplify: 48p73p3\sqrt{\frac{48 p^{7}}{3 p^{3}}}.

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9.2 Exercise 38

Simplify: 75x53x\sqrt{\frac{75 x^{5}}{3 x}}.

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9.2 Exercise 39

Simplify: 72z122z10\sqrt{\frac{72 z^{12}}{2 z^{10}}}.

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9.2 Exercise 40

Simplify: 2164\sqrt{\frac{21}{64}}.

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9.2 Exercise 41

Simplify: 1949\sqrt{\frac{19}{49}}.

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9.2 Exercise 42

Simplify: 2881\sqrt{\frac{28}{81}}.

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9.2 Exercise 44

Simplify: 24p349\sqrt{\frac{24 p^{3}}{49}}.

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9.2 Exercise 45

Simplify: 48x5100\sqrt{\frac{48 x^{5}}{100}}.

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9.2 Exercise 46

Simplify: 45x5y4\sqrt{\frac{45 x^{5}}{y^{4}}}.

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9.2 Exercise 47

Simplify: 80m3n6\sqrt{\frac{80 m^{3}}{n^{6}}}.

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9.2 Exercise 48

Simplify: 54u7v8\sqrt{\frac{54 u^{7}}{v^{8}}}.

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9.2 Exercise 49

Simplify: 81d925d4\sqrt{\frac{81 d^{9}}{25 d^{4}}}.

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9.2 Exercise 50

Simplify: 64x79x3\sqrt{\frac{64 x^{7}}{9 x^{3}}}.

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9.2 Exercise 51

Simplify: 16a9100a5\sqrt{\frac{16 a^{9}}{100 a^{5}}}.

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9.2 Exercise 52

Simplify: 18p5q732pq2\sqrt{\frac{18 p^{5} q^{7}}{32 p q^{2}}}.

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9.2 Exercise 53

Simplify: 50x5y372x4y\sqrt{\frac{50 x^{5} y^{3}}{72 x^{4} y}}.

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9.2 Exercise 54

Simplify: 48m7n2125m5n9\sqrt{\frac{48 m^{7} n^{2}}{125 m^{5} n^{9}}}.

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9.2 Exercise 55

Simplify.

27\sqrt{27}

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9.2 Exercise 57

Simplify.

125\sqrt{125}

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9.2 Exercise 59

Simplify.

200\sqrt{200}

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9.2 Exercise 61

Simplify.

450\sqrt{450}

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9.2 Exercise 63

Simplify.

800\sqrt{800}

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9.2 Exercise 65

Simplify.

675\sqrt{675}

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9.2 Exercise 67

Simplify.

x7\sqrt{x^{7}}

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9.2 Exercise 69

Simplify.

p3\sqrt{p^{3}}

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9.2 Exercise 71

Simplify.

m13\sqrt{m^{13}}

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9.2 Exercise 73

Simplify.

r25\sqrt{r^{25}}

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9.2 Exercise 75

Simplify.

49n17\sqrt{49 n^{17}}

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9.2 Exercise 77

Simplify.

81r15\sqrt{81 r^{15}}

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9.2 Exercise 79

Simplify.

98m5\sqrt{98 m^{5}}

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9.2 Exercise 81

Simplify.

125r13\sqrt{125 r^{13}}

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9.2 Exercise 83

Simplify.

200p13\sqrt{200 p^{13}}

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9.2 Exercise 85

Simplify.

242m23\sqrt{242 m^{23}}

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9.2 Exercise 87

Simplify.

147m7n11\sqrt{147 m^{7} n^{11}}

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9.2 Exercise 89

Simplify.

75r13s9\sqrt{75 r^{13} s^{9}}

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9.2 Exercise 91

Simplify.

300p9q11\sqrt{300 p^{9} q^{11}}

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9.2 Exercise 93

Simplify.

242m13n21\sqrt{242 m^{13} n^{21}}

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9.2 Exercise 95

Simplify.

5+125 + \sqrt{12}

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9.2 Exercise 97

Simplify.

1+451 + \sqrt{45}

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9.2 Exercise 99

Simplify.

10−242\frac{10 - \sqrt{24}}{2}

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9.2 Exercise 101

Simplify.

3+903\frac{3 + \sqrt{90}}{3}

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9.2 Exercise 103

Simplify.

4964\sqrt{\frac{49}{64}}

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9.2 Exercise 105

Simplify.

12116\sqrt{\frac{121}{16}}

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9.2 Exercise 107

Simplify.

7298\sqrt{\frac{72}{98}}

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9.2 Exercise 109

Simplify.

45125\sqrt{\frac{45}{125}}

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9.2 Exercise 111

Simplify.

x10x6\sqrt{\frac{x^{10}}{x^{6}}}

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9.2 Exercise 113

Simplify.

y4y8\sqrt{\frac{y^{4}}{y^{8}}}

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9.2 Exercise 115

Simplify.

200x72x3\sqrt{\frac{200 x^{7}}{2 x^{3}}}

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9.2 Exercise 117

Simplify.

96p96p\sqrt{\frac{96 p^{9}}{6 p}}

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9.2 Exercise 119

Simplify.

3635\sqrt{\frac{36}{35}}

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9.2 Exercise 121

Simplify.

2081\sqrt{\frac{20}{81}}

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9.2 Exercise 123

Simplify.

96x7121\sqrt{\frac{96 x^{7}}{121}}

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9.2 Exercise 125

Simplify.

300m564\sqrt{\frac{300 m^{5}}{64}}

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9.2 Exercise 127

Simplify.

98r5100\sqrt{\frac{98 r^{5}}{100}}

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9.2 Exercise 129

Simplify.

28q6225\sqrt{\frac{28 q^{6}}{225}}

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9.2 Exercise 131

Simplify.

75r9s8\sqrt{\frac{75 r^{9}}{s^{8}}}

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9.2 Exercise 133

Simplify.

28p7q2\sqrt{\frac{28 p^{7}}{q^{2}}}

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9.2 Exercise 135

Simplify.

100x536x3\sqrt{\frac{100 x^{5}}{36 x^{3}}}

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9.2 Exercise 137

Simplify.

121p581p2\sqrt{\frac{121 p^{5}}{81 p^{2}}}

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9.2 Exercise 139

Simplify.

32x5y318x3y\sqrt{\frac{32 x^{5} y^{3}}{18 x^{3} y}}

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9.2 Exercise 141

Simplify.

27p2q108p5q3\sqrt{\frac{27 p^{2} q}{108 p^{5} q^{3}}}

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9.2 Exercise 143

  1. ⓐ Elliott decides to construct a square garden that will take up 288 square feet of his yard. Simplify 288\sqrt{288} to determine the length and the width of his garden. Round to the nearest tenth of a foot.
  2. ⓑ Suppose Elliott decides to reduce the size of his square garden so that he can create a 5-foot-wide walking path on the north and east sides of the garden. Simplify 288−5\sqrt{288} - 5 to determine the length and width…
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9.2 Exercise 145

Explain why x4=x2\sqrt{x^{4}} = x^{2}. Then explain why x16=x8\sqrt{x^{16}} = x^{8}.

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Adapted from Elementary Algebra 2e © 2020 Rice University. Licensed under CC BY 4.0. Source: Elementary Algebra 2e. Imported at revision 77a933c.