AI Tutor
Back to Elementary Algebra 2e

9.5 Divide Square Roots

Reducing a quotient of radicals, then clearing the radical out of a denominator, whether it is a single term or a binomial needing its conjugate.

Elementary Algebra 2e, 9.5 Divide Square Roots

Status
FlagsLoading your progress…

74 exercises

9.5 Exercise 1

Before you get started, take this readiness quiz.

Find a fraction equivalent to 58\frac{5}{8} with denominator 48.
If you missed this problem, review the reference.

2.5

9.5 Exercise 2

Simplify: (5)2\left(\sqrt{5}\right)^{2}.
If you missed this problem, review the reference.

2.5

9.5 Exercise 3

Multiply: (7+3x)(7−3x)\left(7 + 3 x\right) \left(7 - 3 x\right).
If you missed this problem, review the reference.

2.5

9.5 Exercise 4

Simplify: 546\frac{\sqrt{54}}{6}.

2.5

9.5 Exercise 5

Simplify: 328\frac{\sqrt{32}}{8}.

2.5

9.5 Exercise 6

Simplify: 7515\frac{\sqrt{75}}{15}.

2.5

9.5 Exercise 7

Simplify: 6−2412\frac{6 - \sqrt{24}}{12}.

2.5

9.5 Exercise 8

Simplify: 8−4010\frac{8 - \sqrt{40}}{10}.

2.5

9.5 Exercise 9

Simplify: 10−7520\frac{10 - \sqrt{75}}{20}.

2.5

9.5 Exercise 10

Simplify: 2775\frac{\sqrt{27}}{\sqrt{75}}.

2.5

9.5 Exercise 11

Simplify: 48108\frac{\sqrt{48}}{\sqrt{108}}.

2.5

9.5 Exercise 12

Simplify: 9654\frac{\sqrt{96}}{\sqrt{54}}.

2.5

9.5 Exercise 13

Simplify: 6y52y\frac{\sqrt{6 y^{5}}}{\sqrt{2 y}}.

2.5

9.5 Exercise 14

Simplify: 12r36r\frac{\sqrt{12 r^{3}}}{\sqrt{6 r}}.

2.5

9.5 Exercise 15

Simplify: 14p92p5\frac{\sqrt{14 p^{9}}}{\sqrt{2 p^{5}}}.

2.5

9.5 Exercise 16

Simplify: 72x3162x\frac{\sqrt{72 x^{3}}}{\sqrt{162 x}}.

2.5

9.5 Exercise 17

Simplify: 50s3128s\frac{\sqrt{50 s^{3}}}{\sqrt{128 s}}.

2.5

9.5 Exercise 18

Simplify: 75q5108q\frac{\sqrt{75 q^{5}}}{\sqrt{108 q}}.

2.5

9.5 Exercise 19

Simplify: 147ab83a3b4\frac{\sqrt{147 a b^{8}}}{\sqrt{3 a^{3} b^{4}}}.

2.5

9.5 Exercise 20

Simplify: 162x10y22x6y6\frac{\sqrt{162 x^{10} y^{2}}}{\sqrt{2 x^{6} y^{6}}}.

2.5

9.5 Exercise 21

Simplify: 300m3n73m5n\frac{\sqrt{300 m^{3} n^{7}}}{\sqrt{3 m^{5} n}}.

2.5

9.5 Exercise 22

Simplify: 43\frac{4}{\sqrt{3}}.

2.5

9.5 Exercise 23

Simplify: 53\frac{5}{\sqrt{3}}.

2.5

9.5 Exercise 24

Simplify: 65\frac{6}{\sqrt{5}}.

2.5

9.5 Exercise 26

Simplify: 525\frac{5}{2 \sqrt{5}}.

2.5

9.5 Exercise 27

Simplify: −943- \frac{9}{4 \sqrt{3}}.

2.5

9.5 Exercise 29

Simplify: 718\sqrt{\frac{7}{18}}.

2.5

9.5 Exercise 30

Simplify: 332\sqrt{\frac{3}{32}}.

2.5

9.5 Exercise 32

Simplify: 327\sqrt{\frac{3}{27}}.

2.5

9.5 Exercise 33

Simplify: 1050\sqrt{\frac{10}{50}}.

2.5

9.5 Exercise 35

Simplify: 22+3\frac{2}{2 + \sqrt{3}}.

2.5

9.5 Exercise 36

Simplify: 55+3\frac{5}{5 + \sqrt{3}}.

2.5

9.5 Exercise 38

Simplify: 31−5\frac{3}{1 - \sqrt{5}}.

2.5

9.5 Exercise 39

Simplify: 24−6\frac{2}{4 - \sqrt{6}}.

2.5

9.5 Exercise 41

Simplify: 5x+2\frac{\sqrt{5}}{\sqrt{x} + \sqrt{2}}.

2.5

9.5 Exercise 42

Simplify: 10y−3\frac{\sqrt{10}}{\sqrt{y} - \sqrt{3}}.

2.5

9.5 Exercise 44

Simplify: p+2p−2\frac{\sqrt{p} + \sqrt{2}}{\sqrt{p} - \sqrt{2}}.

2.5

9.5 Exercise 45

Simplify: q−10q+10\frac{\sqrt{q} - \sqrt{10}}{\sqrt{q} + \sqrt{10}}.

2.5

9.5 Exercise 46

Simplify.

276\frac{\sqrt{27}}{6}

2.5

9.5 Exercise 48

Simplify.

729\frac{\sqrt{72}}{9}

2.5

9.5 Exercise 50

Simplify.

2−328\frac{2 - \sqrt{32}}{8}

2.5

9.5 Exercise 52

Simplify.

6+456\frac{6 + \sqrt{45}}{6}

2.5

9.5 Exercise 54

Simplify.

80125\frac{\sqrt{80}}{\sqrt{125}}

2.5

9.5 Exercise 56

Simplify.

12872\frac{\sqrt{128}}{\sqrt{72}}

2.5

9.5 Exercise 58

Simplify.

ⓐ 8x62x2\frac{\sqrt{8 x^{6}}}{\sqrt{2 x^{2}}} ⓑ 200m598m\frac{\sqrt{200 m^{5}}}{\sqrt{98 m}}

2.5

9.5 Exercise 60

Simplify.

75r3108r\frac{\sqrt{75 r^{3}}}{\sqrt{108 r}}

2.5

9.5 Exercise 62

Simplify.

108p5q23p3q6\frac{\sqrt{108 p^{5} q^{2}}}{\sqrt{3 p^{3} q^{6}}}

2.5

9.5 Exercise 64

Simplify.

320mn545m7n3\frac{\sqrt{320 m n^{5}}}{\sqrt{45 m^{7} n^{3}}}

2.5

9.5 Exercise 66

Simplify.

9814\frac{\sqrt{98}}{14}

2.5

9.5 Exercise 68

Simplify.

5+12515\frac{5 + \sqrt{125}}{15}

2.5

9.5 Exercise 70

Simplify.

96150\frac{\sqrt{96}}{\sqrt{150}}

2.5

9.5 Exercise 72

Simplify.

26y72y\frac{\sqrt{26 y^{7}}}{\sqrt{2 y}}

2.5

9.5 Exercise 74

Simplify and rationalize the denominator.

106\frac{10}{\sqrt{6}}

2.5

9.5 Exercise 76

Simplify and rationalize the denominator.

67\frac{6}{\sqrt{7}}

2.5

9.5 Exercise 78

Simplify and rationalize the denominator.

313\frac{3}{\sqrt{13}}

2.5

9.5 Exercise 80

Simplify and rationalize the denominator.

10310\frac{10}{3 \sqrt{10}}

2.5

9.5 Exercise 82

Simplify and rationalize the denominator.

495\frac{4}{9 \sqrt{5}}

2.5

9.5 Exercise 84

Simplify and rationalize the denominator.

−923- \frac{9}{2 \sqrt{3}}

2.5

9.5 Exercise 86

Simplify and rationalize the denominator.

320\sqrt{\frac{3}{20}}

2.5

9.5 Exercise 88

Simplify and rationalize the denominator.

740\sqrt{\frac{7}{40}}

2.5

9.5 Exercise 90

Simplify and rationalize the denominator.

19175\sqrt{\frac{19}{175}}

2.5

9.5 Exercise 92

Simplify by rationalizing the denominator.

ⓐ 33+11\frac{3}{3 + \sqrt{11}} ⓑ 81−5\frac{8}{1 - \sqrt{5}}

2.5

9.5 Exercise 94

Simplify by rationalizing the denominator.

ⓐ 55+6\frac{5}{5 + \sqrt{6}} ⓑ 63−7\frac{6}{3 - \sqrt{7}}

2.5

9.5 Exercise 96

Simplify by rationalizing the denominator.

3m−5\frac{\sqrt{3}}{\sqrt{m} - \sqrt{5}}

2.5

9.5 Exercise 98

Simplify by rationalizing the denominator.

2x−6\frac{\sqrt{2}}{\sqrt{x} - \sqrt{6}}

2.5

9.5 Exercise 100

Simplify by rationalizing the denominator.

r+5r−5\frac{\sqrt{r} + \sqrt{5}}{\sqrt{r} - \sqrt{5}}

2.5

9.5 Exercise 102

Simplify by rationalizing the denominator.

150x2y66x4y2\frac{\sqrt{150 x^{2} y^{6}}}{\sqrt{6 x^{4} y^{2}}}

2.5

9.5 Exercise 104

Simplify by rationalizing the denominator.

155\frac{15}{\sqrt{5}}

2.5

9.5 Exercise 106

Simplify by rationalizing the denominator.

854\sqrt{\frac{8}{54}}

2.5

9.5 Exercise 108

Simplify by rationalizing the denominator.

35+5\frac{3}{5 + \sqrt{5}}

2.5

9.5 Exercise 110

Simplify by rationalizing the denominator.

2x−3\frac{\sqrt{2}}{\sqrt{x} - \sqrt{3}}

2.5

9.5 Exercise 112

Simplify by rationalizing the denominator.

x+8x−8\frac{\sqrt{x} + \sqrt{8}}{\sqrt{x} - \sqrt{8}}

2.5

9.5 Exercise 114

A supply kit is dropped from an airplane flying at an altitude of 250 feet. Simplify 25016\sqrt{\frac{250}{16}} to determine how many seconds it takes for the supply kit to reach the ground.

2.5

9.5 Exercise 116

  1. ⓐ Simplify 273\sqrt{\frac{27}{3}} and explain all your steps.
  2. ⓑ Simplify 275\sqrt{\frac{27}{5}} and explain all your steps.
  3. ⓒ Why are the two methods of simplifying square roots different?
2.5

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