Chapter 9 Review Exercises
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Chapter 9 Review Exercises
Simplify and Use Square Roots
Simplify Expressions with Square Roots
In the following exercises, simplify.
√64
√144
- Answer
-
12
−√25
−√81
- Answer
-
−9
√−9
√−36
- Answer
-
not a real number
√64+√225
√64+225
- Answer
-
17
In the following exercises, estimate each square root between two consecutive whole numbers.
√28
√155
- Answer
-
12<√155<13
Approximate Square Roots
In the following exercises, approximate each square root and round to two decimal places.
√15
√57
- Answer
-
7.55
Simplify Variable Expressions with Square Roots
In the following exercises, simplify.
√q2
√64b2
- Answer
-
8b
−√121a2
√225m2n2
- Answer
-
15mn
−√100q2
√49y2
- Answer
-
7y
√4a2b2
√121c2d2
- Answer
-
11cd
Simplify Square Roots
Use the Product Property to Simplify Square Roots
In the following exercises, simplify.
√300
√98
- Answer
-
7√2
√x13
√y19
- Answer
-
y9√y
√16m4
√36n13
- Answer
-
6n6√n
√288m21
√150n7
- Answer
-
5n3√6n
√48r5s4
√108r5s3
- Answer
-
6r2s√3rs
10−√505
6+√726
- Answer
-
1+√2
In the following exercises, simplify.
√1625
√8136
- Answer
-
32
√x8x4
√y6y2
- Answer
-
y2
√98p62p2
√72q82q4
- Answer
-
6q2
√65121
√26169
- Answer
-
√2613
√64x425x2
√36r1016r5
- Answer
-
3r2√r2
√48p3q527pq
√12r5s775r2s
- Answer
-
2rs3√r5
Add and Subtract Square Roots
Add and Subtract Like Square Roots
In the following exercises, simplify.
3√2+√2
5√5+7√5
- Answer
-
12√5
4√y+4√y
6√m−2√m
- Answer
-
4√m
−3√7+2√7−√7
8√13+2√3+3√13
- Answer
-
11√13+2√3
3√5xy−√5xy+3√5xy
2√3rs+√3rs−5√rs
- Answer
-
3√3rs−5√rs
Add and Subtract Square Roots that Need Simplification
In the following exercises, simplify.
√32+3√2
√8+√32
- Answer
-
5√2
√72+√50
√48+√75
- Answer
-
9√3
3√32+√98
13√27−18√192
- Answer
-
0
√50y5−√72y5
Add exercises text here.
- Answer
-
17n2√2
Multiply Square Roots
In the following exercises, simplify.
√2·√20
2√2·6√14
- Answer
-
24√7
√2m2·√20m4
(√62y)(√350y3)
- Answer
-
180y2
(6√3v4)(5√30v)
(√8)2
- Answer
-
8
(−√10)2
(2√5)(5√5)
- Answer
-
50
(−3√3)(5√18)
In the following exercises, simplify.
10(2−√7)
- Answer
-
20−10√7
√3(4+√12)
(5+√2)(3−√2)
- Answer
-
13−2√2
(5−3√7)(1−2√7)
(1−3√x)(5+2√x)
- Answer
-
5−13√x−6x
(3+4√y)(10−√y)
(1+6√p)2
- Answer
-
1+12√p+36p
(2−6√5)2
(3+2√7)(3−2√7)
- Answer
-
−19
(6−√11)(6+√11)
Divide Square Roots
Divide Square Roots
In the following exercises, simplify.
√7510
- Answer
-
√32
2−√126
√48√27
- Answer
-
43
√75x7√3x3
√20y5√2y
- Answer
-
y2√10
√98p6q4√2p4q8
In the following exercises, rationalize the denominator.
10√15
- Answer
-
2√153
6√6
53√5
- Answer
-
√53
102√6
√328
- Answer
-
√2114
√975
In the following exercises, rationalize the denominator.
44+√27
- Answer
-
16−12√3−11
52−√10
42−√5
- Answer
-
−8−4√5
54−√8
√2√p+√3
- Answer
-
√2p−√6p−3
√x−√2√x+√2
Solve Equations with Square Roots
Solve Radical Equations
In the following exercises, solve the equation.
√7z+1=6
- Answer
-
5
√4u−2−4=0
√6m+4−5=0
- Answer
-
72
√2u−3+2=0
√u−4+4=u
- Answer
-
no solution
√v−9+9=0
√r−4−r=−10
- Answer
-
13
√s−9−s=−9
2√2x−7−4=8
- Answer
-
432
√2−x=√2x−7
√a+3=√a+9
- Answer
-
0
√r+3=√r+4
√u+2=√u+5
- Answer
-
116
√n+11−1=√n+4
√y+5+1=√2y+3
- Answer
-
11
In the following exercises, solve. Round approximations to one decimal place.
A pallet of sod will cover an area of about 600 square feet. Trinh wants to order a pallet of sod to make a square lawn in his backyard. Use the formula s=√A to find the length of each side of his lawn.
A helicopter dropped a package from a height of 900 feet above a stranded hiker. Use the formula t=√h4 to find how many seconds it took for the package to reach the hiker.
- Answer
-
7.5 seconds
Officer Morales measured the skid marks of one of the cars involved in an accident. The length of the skid marks was 245 feet. Use the formula s=√24d to find the speed of the car before the brakes were applied.
Higher Roots
Simplify Expressions with Higher Roots
In the following exercises, simplify.
- 6√64
- 3√64
- Answer
-
- 2
- 4
- 3√−27
- 4√−64
- 9√d9
- 8√v8
- Answer
-
- d
- |v|
- 5√a10
- 3√b27
- 4√16x8
- 6√64y12
- Answer
-
- 2x2
- 2y2
- 7√128r14
- 4√81s24
Use the Product Property to Simplify Expressions with Higher Roots
In the following exercises, simplify.
- 9√d9
- Answer
-
- d
- 3√54
- 4√128
- 5√64c8
- 4√48d7
- Answer
-
- 2c5√2c3
- 2d4√3d3
- 3√343q7
- 6√192r9
- 3√−500
- 4√−16
- Answer
-
- −53√4
- not a real number
In the following exercises, simplify.
5√r10r5
3√w12w2
- Answer
-
w33√w
4√64y84y5
3√54z92z3
- Answer
-
3z2
6√64a7b2
In the following exercises, simplify.
45√20−25√20
- Answer
-
25√20
43√18+33√18
4√1250−4√162
- Answer
-
24√2
3√640c5−3√−80c3
\sqrt[5]{96t^8}+\sqrt[5]{486t^4}
- Answer
-
2t^\sqrt[5]{3t^3}+3\sqrt[5]{2t^4}
Rational Exponents
Simplify Expressions with a^{\frac{1}{n}}
In the following exercises, write as a radical expression.
r^{\frac{1}{8}}
s^{\frac{1}{10}}
- Answer
-
In the following exercises, write with a rational exponent.
\sqrt[5]{u}
\sqrt[6]{v}
- Answer
-
v^{\frac{1}{6}}
\sqrt[3]{9m}
\sqrt[6]{10z}
- Answer
-
(10z)^{\frac{1}{6}}
In the following exercises, simplify.
16^{\frac{1}{4}}
32^{\frac{1}{5}}
- Answer
-
2
(−125)^{\frac{1}{3}}
(125)^{−\frac{1}{3}}
- Answer
-
\frac{1}{5}
(−9)^{\frac{1}{2}}
(36)^{−\frac{1}{2}}
- Answer
-
\frac{1}{6}
In the following exercises, write with a rational exponent.
\sqrt[3]{q^5}
\sqrt[5]{n^8}
- Answer
-
n^{\frac{8}{5}}
In the following exercises, simplify.
27^{−\frac{2}{3}}
64^{\frac{5}{2}}
- Answer
-
32,768
36^{\frac{3}{2}}
81^{−\frac{5}{2}}
- Answer
-
\frac{1}{59,049}
Use the Laws of Exponents to Simplify Expressions with Rational Exponents
In the following exercises, simplify.
3^{\frac{4}{5}}·3^{\frac{6}{5}}
(x^6)^{\frac{4}{3}}
- Answer
-
x^8
\frac{z^{\frac{5}{2}}}{z^{\frac{7}{5}}}
(16s^{\frac{9}{4}})^{\frac{1}{4}}
- Answer
-
2s^{\frac{9}{16}}
(m^{8}n^{12})^{\frac{1}{4}}
\frac{z^{\frac{2}{3}}·z^{−\frac{1}{3}}}{z^{−\frac{5}{3}}}
- Answer
-
z^2
Practice Test
In the following exercises, simplify.
\sqrt{81+144}
\sqrt{169m^{4}n^{2}}
- Answer
-
13m^{2}|n|
\sqrt{36n^{13}}
3\sqrt{13}+5\sqrt{2}+\sqrt{13}
- Answer
-
4\sqrt{13}+5\sqrt{2}
5\sqrt{20}+2\sqrt{125}
(3\sqrt{6y})(\sqrt{250y^3})
- Answer
-
180y^2\sqrt{3}
(2−5\sqrt{x})(3+\sqrt{x})
(1−2\sqrt{q})^2
- Answer
-
1−4\sqrt{q}+4q
- \sqrt{a^{12}}
- \sqrt[3]{b^{21}}
- \sqrt[4]{81x^{12}}
- \sqrt[6]{64y^{18}}
- Answer
-
- 3x^3
- 2y^3
\sqrt[6]{\frac{64r^{12}}{25r^6}}
\sqrt{\frac{14y^3}{7y}}
- Answer
-
y\sqrt{2}
\frac{\sqrt{256x^7}}{\sqrt{54x^2}}
\sqrt[4]{512}−2\sqrt[4]{32}
- Answer
-
0
- 256^{\frac{1}{4}}
- 243^{\frac{1}{5}}
49^{\frac{3}{2}}
- Answer
-
343
25^{−\frac{5}{2}}
\frac{w^{\frac{3}{4}}}{w^{\frac{7}{4}}}
- Answer
-
\frac{1}{w}
(27s^{\frac{3}{5}})^{\frac{1}{3}}
In the following exercises, rationalize the denominator.
\frac{3}{2\sqrt{6}}
- Answer
-
\frac{\sqrt{6}}{4}
\frac{\sqrt{3}}{\sqrt{x}+\sqrt{5}}
In the following exercises, solve.
3\sqrt{2x−3}−20=7
- Answer
-
42
\sqrt{3u−2}=\sqrt{5u+1}
In the following exercise, solve.
A helicopter flying at an altitude of 600 feet dropped a package to a lifeboat. Use the formula t=\frac{\sqrt{h}}{4} to find how many seconds it took for the package to reach the hiker. Round your answer to the nearest tenth of a second.
- Answer
-
6.1 seconds