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9.1 Solve Quadratic Equations Using the Square Root Property

Taking roots of both sides when the equation reads ax^2 = k or a(x-h)^2 = k, producing paired answers that may be irrational or imaginary.

Intermediate Algebra 2e, 9.1 Solve Quadratic Equations Using the Square Root Property

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61 exercises

9.1 Exercise 1

Before you get started, take this readiness quiz.

Simplify: 128.\sqrt{128} .
If you missed this problem, review the reference.

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9.1 Exercise 2

Simplify: 325\sqrt{\frac{32}{5}}.
If you missed this problem, review the reference.

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9.1 Exercise 3

Factor: 9x2−12x+49 x^{2} - 12 x + 4.
If you missed this problem, review the reference.

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9.1 Exercise 5

Solve: x2−48=0.x^{2} - 48 = 0 .

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9.1 Exercise 6

Solve: y2−27=0.y^{2} - 27 = 0 .

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9.1 Exercise 8

Solve: 2x2=98.2 x^{2} = 98 .

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9.1 Exercise 9

Solve: 5m2=80.5 m^{2} = 80 .

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9.1 Exercise 11

Solve: c2+12=0.c^{2} + 12 = 0 .

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9.1 Exercise 12

Solve: q2+24=0.q^{2} + 24 = 0 .

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9.1 Exercise 14

Solve: 12x2+4=24.\frac{1}{2} x^{2} + 4 = 24 .

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9.1 Exercise 15

Solve: 34y2−3=18.\frac{3}{4} y^{2} - 3 = 18 .

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9.1 Exercise 17

Solve: 5r2−2=34.5 r^{2} - 2 = 34 .

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9.1 Exercise 18

Solve: 3t2+6=70.3 t^{2} + 6 = 70 .

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9.1 Exercise 20

Solve: 3(a−3)2=54.3 \left(a - 3\right)^{2} = 54 .

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9.1 Exercise 21

Solve: 2(b+2)2=80.2 \left(b + 2\right)^{2} = 80 .

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9.1 Exercise 22

Solve: (x−13)2=59.\left(x - \frac{1}{3}\right)^{2} = \frac{5}{9} .

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9.1 Exercise 23

Solve: (x−12)2=54.\left(x - \frac{1}{2}\right)^{2} = \frac{5}{4} .

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9.1 Exercise 24

Solve: (y+34)2=716.\left(y + \frac{3}{4}\right)^{2} = \frac{7}{16} .

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9.1 Exercise 25

Solve: 2(x−2)2+3=57.2 \left(x - 2\right)^{2} + 3 = 57 .

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9.1 Exercise 26

Solve: 5(a−5)2+4=104.5 \left(a - 5\right)^{2} + 4 = 104 .

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9.1 Exercise 27

Solve: 3(b+3)2−8=88.3 \left(b + 3\right)^{2} - 8 = 88 .

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9.1 Exercise 28

Solve: (2x−3)2=−12.\left(2 x - 3\right)^{2} = −12 .

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9.1 Exercise 29

Solve: (3r+4)2=−8.\left(3 r + 4\right)^{2} = −8 .

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9.1 Exercise 30

Solve: (2t−8)2=−10.\left(2 t - 8\right)^{2} = −10 .

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9.1 Exercise 32

Solve: 9m2−12m+4=25.9 m^{2} - 12 m + 4 = 25 .

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9.1 Exercise 33

Solve: 16n2+40n+25=4.16 n^{2} + 40 n + 25 = 4 .

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9.1 Exercise 34

Solve each equation.

a2=49a^{2} = 49

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9.1 Exercise 36

Solve each equation.

r2−24=0r^{2} - 24 = 0

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9.1 Exercise 38

Solve each equation.

u2−300=0u^{2} - 300 = 0

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9.1 Exercise 40

Solve each equation.

4m2=364 m^{2} = 36

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9.1 Exercise 42

Solve each equation.

43x2=48\frac{4}{3} x^{2} = 48

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9.1 Exercise 44

Solve each equation.

x2+25=0x^{2} + 25 = 0

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9.1 Exercise 46

Solve each equation.

x2+63=0x^{2} + 63 = 0

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9.1 Exercise 48

Solve each equation.

43x2+2=110\frac{4}{3} x^{2} + 2 = 110

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9.1 Exercise 50

Solve each equation.

25a2+3=11\frac{2}{5} a^{2} + 3 = 11

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9.1 Exercise 52

Solve each equation.

7p2+10=267 p^{2} + 10 = 26

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9.1 Exercise 54

Solve each equation.

5y2−7=255 y^{2} - 7 = 25

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9.1 Exercise 56

Solve each equation.

(u−6)2=64\left(u - 6\right)^{2} = 64

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9.1 Exercise 58

Solve each equation.

(m−6)2=20\left(m - 6\right)^{2} = 20

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9.1 Exercise 60

Solve each equation.

(r−12)2=34\left(r - \frac{1}{2}\right)^{2} = \frac{3}{4}

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9.1 Exercise 62

Solve each equation.

(y+23)2=881\left(y + \frac{2}{3}\right)^{2} = \frac{8}{81}

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9.1 Exercise 64

Solve each equation.

(a−7)2+5=55\left(a - 7\right)^{2} + 5 = 55

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9.1 Exercise 66

Solve each equation.

4(x+3)2−5=274 \left(x + 3\right)^{2} - 5 = 27

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9.1 Exercise 68

Solve each equation.

(5c+1)2=−27\left(5 c + 1\right)^{2} = −27

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9.1 Exercise 70

Solve each equation.

(4x−3)2+11=−17\left(4 x - 3\right)^{2} + 11 = −17

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9.1 Exercise 72

Solve each equation.

m2−4m+4=8m^{2} - 4 m + 4 = 8

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9.1 Exercise 74

Solve each equation.

x2−6x+9=12x^{2} - 6 x + 9 = 12

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9.1 Exercise 76

Solve each equation.

25x2−30x+9=3625 x^{2} - 30 x + 9 = 36

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9.1 Exercise 78

Solve each equation.

36x2−24x+4=8136 x^{2} - 24 x + 4 = 81

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9.1 Exercise 80

Solve using the Square Root Property.

2r2=322 r^{2} = 32

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9.1 Exercise 82

Solve using the Square Root Property.

(a−4)2=28\left(a - 4\right)^{2} = 28

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9.1 Exercise 84

Solve using the Square Root Property.

9w2−24w+16=19 w^{2} - 24 w + 16 = 1

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9.1 Exercise 86

Solve using the Square Root Property.

a2−18=0a^{2} - 18 = 0

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9.1 Exercise 88

Solve using the Square Root Property.

(p−13)2=79\left(p - \frac{1}{3}\right)^{2} = \frac{7}{9}

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9.1 Exercise 90

Solve using the Square Root Property.

m2+12=0m^{2} + 12 = 0

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9.1 Exercise 92

Solve using the Square Root Property.

u2−14u+49=72u^{2} - 14 u + 49 = 72

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9.1 Exercise 94

Solve using the Square Root Property.

(m−4)2+3=15\left(m - 4\right)^{2} + 3 = 15

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9.1 Exercise 96

Solve using the Square Root Property.

(x+5)2=4\left(x + 5\right)^{2} = 4

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9.1 Exercise 98

Solve using the Square Root Property.

6c2+4=296 c^{2} + 4 = 29

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9.1 Exercise 100

Solve using the Square Root Property.

(x−6)2+7=3\left(x - 6\right)^{2} + 7 = 3

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9.1 Exercise 102

In your own words, explain the Square Root Property.

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