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.
√10√2
- Answer
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2√5
√6√8
√18√40
- Answer
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12√5
√11√11
√y√y
- Answer
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y
√r3√r3
√m+3√m+3
- Answer
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m+3
√a−7√a−7
√x2+4x+4
- Answer
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x+2
√y2−12y+36
√x+5√x+2
- Answer
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√(x+5)(x+2)x+2
√n−3√n−1
√50√2
- Answer
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5
√755√3
√a2+6a+9√a+3
- Answer
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√a+3
√4x2+4x+1√2x+1
√x2−11x+24√x−8
- Answer
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√x−3
√y2+11y+28√y+4
√3(√5+√3)
- Answer
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3+√15
√5(√6−√10)
√a(√a−√bc)
- Answer
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a−√abc
√x(√x5−√3x)
√7a3(√2a−√4a3)
- Answer
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a2√14−2a3√7
3√7
2√5
- Answer
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2√55
6√2
8y√y
- Answer
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8√y
16a2√5a
(2+√3)(2−√3)
- Answer
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1
(x+√8)(3x+√8)
(4y−√3x)(4y+√3x)
- Answer
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16y2−3x
(6r+√2s)(4r+√2s)
22+√7
- Answer
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−2(2−√7)3
41−√6
6x+√y
- Answer
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6(x−√y)x2−y
10a−√2b
√5a+√3
- Answer
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a√5−√15a2−3
√21+√10
8+√32+√6
- Answer
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8√6−2√3+3√2−162
4+√114−√11
√36a4b5c11x2y5
- Answer
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6a2b2c5√bcyxy3
√x12y10z8w7
√32x5y(x−2)3
- Answer
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4x2(x−2)√2xy(x−2)
−2√60r4s3
√316
- Answer
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√34
√425
√916
- Answer
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34
√536
√16
- Answer
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√66
√310
√(x+4)4(x−1)5
- Answer
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(x+4)2(x−1)2(√x−1)
√(3x+5)3(2x−7)3
√(y−3z)12(y+3z)10(y−5z)3
- Answer
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(y−3z)6(y+3z)5(y−5z)√y−5z
√(8a−5b)26(2a−9b)40(a−b)15
4√11+8√11
- Answer
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12√11
−√6+5√6
5√60−7√15
- Answer
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3√15
4ax2√75x4+6a√3x8
−3√54−16√96
- Answer
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−73√6
√18x2y√2x2y
√4x2+32x+64+√10x2+80x+160
- Answer
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(2+√10)(x+4)
−2√9x2−42x+49+5√18x2−84x+98
−10√56a3b7+2a2b√126ab5
- Answer
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(−20ab3+6a2b3)√14ab
√3x−√5x√7x+√2x
√6a+√2a√3a−√5a
- Answer
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−3√2−√30−√6−√102
Square Root Equations with Applications
For the following problems, solve the equations.
√3x=9
√4a=16
- Answer
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a=64
√x+7=4
√a+6=−5
- Answer
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No Solution
√4a+5=21
√3m+7=10
- Answer
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m=31
√y+10=5
√a−7=6
- Answer
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a=43
√4x−8=x−2
√2x+3+8=11
- Answer
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x=3
√a2+5+5=a
√5b+4−5=−2
- Answer
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b=1
√2a+1−10=−3
√2x+5=√x+3
- Answer
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x=−2
√5a−11
At a small business, the monthly number of sales S is approximately related to the number of employees E by S=140+8√E−2
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
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a) S=180
b) E=258
The resonance frequency f in an electronic circuit containing inductance L and capacitance C in series is given by:
f=12π√LC
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.
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=mm′r2
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
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a) F=15.8125
b) r=12.31 cm