AI Tutor
Back to Elementary Algebra 2e

9.3 Add and Subtract Square Roots

Like radicals behave like like terms, so the work is simplifying each radical first until sums that looked uncombinable collapse.

Elementary Algebra 2e, 9.3 Add and Subtract Square Roots

Status
FlagsLoading your progress…

91 exercises

9.3 Exercise 1

Before you get started, take this readiness quiz.

Add: ⓐ 3x+9x3 x + 9 x ⓑ 5m+5n5 m + 5 n.
If you missed this problem, review the reference.

2.5

9.3 Exercise 2

Simplify: 50x3\sqrt{50 x^{3}}.
If you missed this problem, review the reference.

2.5

9.3 Exercise 3

Simplify: 22−722 \sqrt{2} - 7 \sqrt{2}.

2.5

9.3 Exercise 4

Simplify: 82−928 \sqrt{2} - 9 \sqrt{2}.

2.5

9.3 Exercise 5

Simplify: 53−935 \sqrt{3} - 9 \sqrt{3}.

2.5

9.3 Exercise 6

Simplify: 3y+4y3 \sqrt{y} + 4 \sqrt{y}.

2.5

9.3 Exercise 7

Simplify: 2x+7x2 \sqrt{x} + 7 \sqrt{x}.

2.5

9.3 Exercise 8

Simplify: 5u+3u5 \sqrt{u} + 3 \sqrt{u}.

2.5

9.3 Exercise 9

Simplify: 4x−2y4 \sqrt{x} - 2 \sqrt{y}.

2.5

9.3 Exercise 10

Simplify: 7p−6q7 \sqrt{p} - 6 \sqrt{q}.

2.5

9.3 Exercise 11

Simplify: 6a−3b6 \sqrt{a} - 3 \sqrt{b}.

2.5

9.3 Exercise 12

Simplify: 513+413+2135 \sqrt{13} + 4 \sqrt{13} + 2 \sqrt{13}.

2.5

9.3 Exercise 13

Simplify: 411+211+3114 \sqrt{11} + 2 \sqrt{11} + 3 \sqrt{11}.

2.5

9.3 Exercise 14

Simplify: 610+210+3106 \sqrt{10} + 2 \sqrt{10} + 3 \sqrt{10}.

2.5

9.3 Exercise 15

Simplify: 26−66+332 \sqrt{6} - 6 \sqrt{6} + 3 \sqrt{3}.

2.5

9.3 Exercise 16

Simplify: 55−45+265 \sqrt{5} - 4 \sqrt{5} + 2 \sqrt{6}.

2.5

9.3 Exercise 17

Simplify: 37−87+253 \sqrt{7} - 8 \sqrt{7} + 2 \sqrt{5}.

2.5

9.3 Exercise 18

Simplify: 25n−65n+45n2 \sqrt{5 n} - 6 \sqrt{5 n} + 4 \sqrt{5 n}.

2.5

9.3 Exercise 19

Simplify: 7x−77x+47x\sqrt{7 x} - 7 \sqrt{7 x} + 4 \sqrt{7 x}.

2.5

9.3 Exercise 20

Simplify: 43y−73y+23y4 \sqrt{3 y} - 7 \sqrt{3 y} + 2 \sqrt{3 y}.

2.5

9.3 Exercise 21

Simplify: 3xy+53xy−43xy\sqrt{3 x y} + 5 \sqrt{3 x y} - 4 \sqrt{3 x y}.

2.5

9.3 Exercise 22

Simplify: 5xy+45xy−75xy\sqrt{5 x y} + 4 \sqrt{5 x y} - 7 \sqrt{5 x y}.

2.5

9.3 Exercise 23

Simplify: 37mn+7mn−47mn3 \sqrt{7 m n} + \sqrt{7 m n} - 4 \sqrt{7 m n}.

2.5

9.3 Exercise 24

Simplify: 20+35\sqrt{20} + 3 \sqrt{5}.

2.5

9.3 Exercise 25

Simplify: 18+62\sqrt{18} + 6 \sqrt{2}.

2.5

9.3 Exercise 26

Simplify: 27+43\sqrt{27} + 4 \sqrt{3}.

2.5

9.3 Exercise 27

Simplify: 48−75\sqrt{48} - \sqrt{75}.

2.5

9.3 Exercise 28

Simplify: 32−18\sqrt{32} - \sqrt{18}.

2.5

9.3 Exercise 29

Simplify: 20−45\sqrt{20} - \sqrt{45}.

2.5

9.3 Exercise 30

Simplify: 518−285 \sqrt{18} - 2 \sqrt{8}.

2.5

9.3 Exercise 31

Simplify: 427−3124 \sqrt{27} - 3 \sqrt{12}.

2.5

9.3 Exercise 32

Simplify: 320−7453 \sqrt{20} - 7 \sqrt{45}.

2.5

9.3 Exercise 33

Simplify: 34192−56108\frac{3}{4} \sqrt{192} - \frac{5}{6} \sqrt{108}.

2.5

9.3 Exercise 34

Simplify: 23108−57147\frac{2}{3} \sqrt{108} - \frac{5}{7} \sqrt{147}.

2.5

9.3 Exercise 35

Simplify: 35200−34128\frac{3}{5} \sqrt{200} - \frac{3}{4} \sqrt{128}.

2.5

9.3 Exercise 36

Simplify: 2348−3412\frac{2}{3} \sqrt{48} - \frac{3}{4} \sqrt{12}.

2.5

9.3 Exercise 37

Simplify: 2532−138\frac{2}{5} \sqrt{32} - \frac{1}{3} \sqrt{8}.

2.5

9.3 Exercise 38

Simplify: 1380−14125\frac{1}{3} \sqrt{80} - \frac{1}{4} \sqrt{125}.

2.5

9.3 Exercise 39

Simplify: 18n5−32n5\sqrt{18 n^{5}} - \sqrt{32 n^{5}}.

2.5

9.3 Exercise 40

Simplify: 32m7−50m7\sqrt{32 m^{7}} - \sqrt{50 m^{7}}.

2.5

9.3 Exercise 41

Simplify: 27p3−48p3\sqrt{27 p^{3}} - \sqrt{48 p^{3}}.

2.5

9.3 Exercise 42

Simplify: 950m2−648m29 \sqrt{50 m^{2}} - 6 \sqrt{48 m^{2}}.

2.5

9.3 Exercise 43

Simplify: 532x2−348x25 \sqrt{32 x^{2}} - 3 \sqrt{48 x^{2}}.

2.5

9.3 Exercise 44

Simplify: 748y2−472y27 \sqrt{48 y^{2}} - 4 \sqrt{72 y^{2}}.

2.5

9.3 Exercise 45

Simplify: 28x2−5x32+518x22 \sqrt{8 x^{2}} - 5 x \sqrt{32} + 5 \sqrt{18 x^{2}}.

2.5

9.3 Exercise 46

Simplify: 312x2−2x48+427x23 \sqrt{12 x^{2}} - 2 x \sqrt{48} + 4 \sqrt{27 x^{2}}.

2.5

9.3 Exercise 47

Simplify: 318x2−6x32+250x23 \sqrt{18 x^{2}} - 6 x \sqrt{32} + 2 \sqrt{50 x^{2}}.

2.5

9.3 Exercise 48

Simplify.

82−528 \sqrt{2} - 5 \sqrt{2}

2.5

9.3 Exercise 50

Simplify.

35+653 \sqrt{5} + 6 \sqrt{5}

2.5

9.3 Exercise 52

Simplify.

97−1079 \sqrt{7} - 10 \sqrt{7}

2.5

9.3 Exercise 54

Simplify.

7y+2y7 \sqrt{y} + 2 \sqrt{y}

2.5

9.3 Exercise 56

Simplify.

a−4a\sqrt{a} - 4 \sqrt{a}

2.5

9.3 Exercise 58

Simplify.

5c+2c5 \sqrt{c} + 2 \sqrt{c}

2.5

9.3 Exercise 60

Simplify.

8a−2b8 \sqrt{a} - 2 \sqrt{b}

2.5

9.3 Exercise 62

Simplify.

5m+n5 \sqrt{m} + \sqrt{n}

2.5

9.3 Exercise 64

Simplify.

87+27+378 \sqrt{7} + 2 \sqrt{7} + 3 \sqrt{7}

2.5

9.3 Exercise 66

Simplify.

311+211−8113 \sqrt{11} + 2 \sqrt{11} - 8 \sqrt{11}

2.5

9.3 Exercise 68

Simplify.

33−83+753 \sqrt{3} - 8 \sqrt{3} + 7 \sqrt{5}

2.5

9.3 Exercise 70

Simplify.

62+22−356 \sqrt{2} + 2 \sqrt{2} - 3 \sqrt{5}

2.5

9.3 Exercise 72

Simplify.

32a−42a+52a3 \sqrt{2 a} - 4 \sqrt{2 a} + 5 \sqrt{2 a}

2.5

9.3 Exercise 74

Simplify.

83c+23c−93c8 \sqrt{3 c} + 2 \sqrt{3 c} - 9 \sqrt{3 c}

2.5

9.3 Exercise 76

Simplify.

53ab+3ab−23ab5 \sqrt{3 a b} + \sqrt{3 a b} - 2 \sqrt{3 a b}

2.5

9.3 Exercise 78

Simplify.

2pq−5pq+4pq2 \sqrt{p q} - 5 \sqrt{p q} + 4 \sqrt{p q}

2.5

9.3 Exercise 80

Simplify.

50+42\sqrt{50} + 4 \sqrt{2}

2.5

9.3 Exercise 82

Simplify.

80−35\sqrt{80} - 3 \sqrt{5}

2.5

9.3 Exercise 84

Simplify.

27−75\sqrt{27} - \sqrt{75}

2.5

9.3 Exercise 86

Simplify.

48+27\sqrt{48} + \sqrt{27}

2.5

9.3 Exercise 88

Simplify.

250−3722 \sqrt{50} - 3 \sqrt{72}

2.5

9.3 Exercise 90

Simplify.

212+3482 \sqrt{12} + 3 \sqrt{48}

2.5

9.3 Exercise 92

Simplify.

2372+1550\frac{2}{3} \sqrt{72} + \frac{1}{5} \sqrt{50}

2.5

9.3 Exercise 94

Simplify.

1220−2345\frac{1}{2} \sqrt{20} - \frac{2}{3} \sqrt{45}

2.5

9.3 Exercise 96

Simplify.

1627−3848\frac{1}{6} \sqrt{27} - \frac{3}{8} \sqrt{48}

2.5

9.3 Exercise 98

Simplify.

1498−13128\frac{1}{4} \sqrt{98} - \frac{1}{3} \sqrt{128}

2.5

9.3 Exercise 100

Simplify.

72a5−50a5\sqrt{72 a^{5}} - \sqrt{50 a^{5}}

2.5

9.3 Exercise 102

Simplify.

80c7−20c7\sqrt{80 c^{7}} - \sqrt{20 c^{7}}

2.5

9.3 Exercise 104

Simplify.

980p4−698p49 \sqrt{80 p^{4}} - 6 \sqrt{98 p^{4}}

2.5

9.3 Exercise 106

Simplify.

250r8+454r82 \sqrt{50 r^{8}} + 4 \sqrt{54 r^{8}}

2.5

9.3 Exercise 108

Simplify.

320x2−445x2+5x803 \sqrt{20 x^{2}} - 4 \sqrt{45 x^{2}} + 5 x \sqrt{80}

2.5

9.3 Exercise 110

Simplify.

3128y2+4y162−898y23 \sqrt{128 y^{2}} + 4 y \sqrt{162} - 8 \sqrt{98 y^{2}}

2.5

9.3 Exercise 112

Mixed Practice

28+68−582 \sqrt{8} + 6 \sqrt{8} - 5 \sqrt{8}

2.5

9.3 Exercise 114

Mixed Practice

175k4−63k4\sqrt{175 k^{4}} - \sqrt{63 k^{4}}

2.5

9.3 Exercise 116

Mixed Practice

2363−23002 \sqrt{363} - 2 \sqrt{300}

2.5

9.3 Exercise 118

Mixed Practice

92−829 \sqrt{2} - 8 \sqrt{2}

2.5

9.3 Exercise 120

Mixed Practice

813−413−3138 \sqrt{13} - 4 \sqrt{13} - 3 \sqrt{13}

2.5

9.3 Exercise 122

Mixed Practice

80a5−45a5\sqrt{80 a^{5}} - \sqrt{45 a^{5}}

2.5

9.3 Exercise 124

Mixed Practice

2119−21921 \sqrt{19} - 2 \sqrt{19}

2.5

9.3 Exercise 126

Mixed Practice

5627+5848\frac{5}{6} \sqrt{27} + \frac{5}{8} \sqrt{48}

2.5

9.3 Exercise 128

Mixed Practice

75−108\sqrt{75} - \sqrt{108}

2.5

9.3 Exercise 130

Mixed Practice

424x2−54x2+3x64 \sqrt{24 x^{2}} - \sqrt{54 x^{2}} + 3 x \sqrt{6}

2.5

9.3 Exercise 132

A decorator decides to use square tiles as an accent strip in the design of a new shower, but she wants to rotate the tiles to look like diamonds. She will use 9 large tiles that measure 8 inches on a side and 8 small tiles that measure 2 inches on a side. Determine the width of the accent strip by simplifying the expression 9(82)+8(22)9 \left(8 \sqrt{2}\right) + 8 \left(2 \sqrt{2}\right). (Round to the nearest tenth of an inch.)

2.5

9.3 Exercise 134

Explain the difference between like radicals and unlike radicals. Make sure your answer makes sense for radicals containing both numbers and variables.

2.5

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