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Mathematics LibreTexts

9.9: Exercise Supplement

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Exercise Supplement

Square Root Expressions - Addition and Subtraction of Square Root Expressions

For the following problems, simplify the expressions.

Exercise 9.9.1

102

Answer

25

Exercise 9.9.2

68

Exercise 9.9.3

1840

Answer

125

Exercise 9.9.4

1111

Exercise 9.9.5

yy

Answer

y

Exercise 9.9.6

r3r3

Exercise 9.9.7

m+3m+3

Answer

m+3

Exercise 9.9.8

a7a7

Exercise 9.9.9

x2+4x+4

Answer

x+2

Exercise 9.9.10

y212y+36

Exercise 9.9.11

x+5x+2

Answer

(x+5)(x+2)x+2

Exercise 9.9.12

n3n1

Exercise 9.9.13

502

Answer

5

Exercise 9.9.14

7553

Exercise 9.9.15

a2+6a+9a+3

Answer

a+3

Exercise 9.9.16

4x2+4x+12x+1

Exercise 9.9.17

x211x+24x8

Answer

x3

Exercise 9.9.18

y2+11y+28y+4

Exercise 9.9.19

3(5+3)

Answer

3+15

Exercise 9.9.20

5(610)

Exercise 9.9.21

a(abc)

Answer

aabc

Exercise 9.9.22

x(x53x)

Exercise 9.9.23

7a3(2a4a3)

Answer

a2142a37

Exercise 9.9.24

37

Exercise 9.9.25

25

Answer

255

Exercise 9.9.26

62

Exercise 9.9.27

8yy

Answer

8y

Exercise 9.9.28

16a25a

Exercise 9.9.29

(2+3)(23)

Answer

1

Exercise 9.9.30

(x+8)(3x+8)

Exercise 9.9.31

(4y3x)(4y+3x)

Answer

16y23x

Exercise 9.9.32

(6r+2s)(4r+2s)

Exercise 9.9.33

22+7

Answer

2(27)3

Exercise 9.9.34

416

Exercise 9.9.35

6x+y

Answer

6(xy)x2y

Exercise 9.9.36

10a2b

Exercise 9.9.37

5a+3

Answer

a515a23

Exercise 9.9.38

21+10

Exercise 9.9.39

8+32+6

Answer

8623+32162

Exercise 9.9.40

4+11411

Exercise 9.9.41

36a4b5c11x2y5

Answer

6a2b2c5bcyxy3

Exercise 9.9.42

x12y10z8w7

Exercise 9.9.43

32x5y(x2)3

Answer

4x2(x2)2xy(x2)

Exercise 9.9.44

260r4s3

Exercise 9.9.45

316

Answer

34

Exercise 9.9.46

425

Exercise 9.9.47

916

Answer

34

Exercise 9.9.48

536

Exercise 9.9.49

16

Answer

66

Exercise 9.9.50

310

Exercise 9.9.51

(x+4)4(x1)5

Answer

(x+4)2(x1)2(x1)

Exercise 9.9.52

(3x+5)3(2x7)3

Exercise 9.9.53

(y3z)12(y+3z)10(y5z)3

Answer

(y3z)6(y+3z)5(y5z)y5z

Exercise 9.9.54

(8a5b)26(2a9b)40(ab)15

Exercise 9.9.55

411+811

Answer

1211

Exercise 9.9.56

6+56

Exercise 9.9.57

560715

Answer

315

Exercise 9.9.58

4ax275x4+6a3x8

Exercise 9.9.59

3541696

Answer

736

Exercise 9.9.60

18x2y2x2y

Exercise 9.9.61

4x2+32x+64+10x2+80x+160

Answer

(2+10)(x+4)

Exercise 9.9.62

29x242x+49+518x284x+98

Exercise 9.9.63

1056a3b7+2a2b126ab5

Answer

(20ab3+6a2b3)14ab

Exercise 9.9.64

3x5x7x+2x

Exercise 9.9.65

6a+2a3a5a

Answer

32306102

Square Root Equations with Applications

For the following problems, solve the equations.

Exercise 9.9.66

3x=9

Exercise 9.9.67

4a=16

Answer

a=64

Exercise 9.9.68

x+7=4

Exercise 9.9.69

a+6=5

Answer

No Solution

Exercise 9.9.70

4a+5=21

Exercise 9.9.71

3m+7=10

Answer

m=31

Exercise 9.9.72

y+10=5

Exercise 9.9.73

a7=6

Answer

a=43

Exercise 9.9.74

4x8=x2

Exercise 9.9.75

2x+3+8=11

Answer

x=3

Exercise 9.9.76

a2+5+5=a

Exercise 9.9.77

5b+45=2

Answer

b=1

Exercise 9.9.78

2a+110=3

Exercise 9.9.79

2x+5=x+3

Answer

x=2

Exercise 9.9.80

5a11

Exercise 9.9.81

At a small business, the monthly number of sales S is approximately related to the number of employees E by S=140+8E2

a) Determine the approximate number of sales if the number of employees is 27.

b) Determine the approximate number of employees if the monthly sales are 268.

Answer

a) S=180

b) E=258

Exercise 9.9.82

The resonance frequency f in an electronic circuit containing inductance L and capacitance C in series is given by:

f=12πLC

a) Determine the resonance frequency in an electronic circuit if the inductance is 9 and the capacitance is 0.0001. Use π=3.14.

b) Determine the inductance in an electric circuit if the resonance frequency is 5.308 and the capacitance is 0.0001. Use π=3.14.

Exercise 9.9.83

If two magnetic poles of strength m and m are at a distance r centimeters (cm) apart, the force \9F\) of repulsion in air between them is given by:

F=mmr2

a) Determine the force of repulsion if two magnetic poles of strengths 22 and 46 units are 8 cm apart.

b) Determine how far apart are two magnetic poles of strengths 14 and 16 units if the force of repulsion in air between them is 42 units.

Answer

a) F=15.8125  

b) r=12.31 cm


This page titled 9.9: Exercise Supplement is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Denny Burzynski & Wade Ellis, Jr. (OpenStax CNX) .

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