AnswersFL-1200700-Mathematics for College Algebra MISRadical Equations and Extraneous Roots

Radical Equations and Extraneous Roots — Unit test Answers

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Which expression is equivalent to ?

Question illustration
A
StartFraction RootIndex 12 StartRoot 27 EndRoot Over 2 EndFraction
Option A
B
StartFraction RootIndex 4 StartRoot 24 EndRoot Over 2 EndFraction
Option B
C
StartFraction RootIndex 12 StartRoot 55296 EndRoot Over 2 EndFraction
Option C
D
StartFraction RootIndex 12 StartRoot 177147 EndRoot Over 3 EndFraction
Option D
2
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The speed that a tsunami can travel is modeled by the equation , where S is the speed in kilometers per hour and d is the average depth of the water in kilometers. What is the approximate depth of water for a tsunami traveling at 200 kilometers per hour?

Question illustration
A
0.32 km
B
0.75 km
C
1.12 km
D
3.17 km
3

What is the following quotient?

Question illustration
A
StartFraction 9 StartRoot 7 EndRoot + StartRoot 14 EndRoot Over negative 3 EndFraction
Option A
B
StartFraction 36 minus 9 StartRoot 7 EndRoot + 4 StartRoot 2 EndRoot minus StartRoot 14 EndRoot EndFraction
Option B
C
StartFraction 36 + 9 StartRoot 7 EndRoot + 4 StartRoot 2 EndRoot + StartRoot 14 EndRoot Over 9 EndFraction
Option C
D
StartFraction 79 Over 9 EndFraction
Option D
4

What is the solution of ?

Question illustration
A
x = –3
B
x = 4
C
x = –3 or x = 4
D
no solution
5

Kaylib’s eye-level height is 48 ft above sea level, and Addison’s eye-level height is ft above sea level. How much farther can Addison see to the horizon? Use the formula , with d being the distance they can see in miles and h being their eye-level height in feet.

Question illustration
A
mi
Option A
B
mi
Option B
C
mi
Option C
D
mi
Option D
6

Which function is undefined for x = 0?

A
y = RootIndex 3 StartRoot x minus 2 EndRoot
Option A
B
y = StartRoot x minus 2 EndRoot
Option B
C
y = RootIndex 3 StartRoot x + 2 EndRoot
Option C
D
y = StartRoot x + 2 EndRoot
Option D
7

What is the following product? Assume

Question illustration
A
80 x Superscript 4 Baseline + 8 x Superscript 4 Baseline StartRoot 30 x EndRoot + 24 x Superscript 4
Option A
B
80 x Superscript 6 Baseline + 8 x Superscript 5 Baseline + 8 x Superscript 5 Baseline StartRoot 30 EndRoot + 24 x Superscript 4
Option B
C
104 x Superscript 4
Option C
D
104 x Superscript 4 + 16 x Superscript 4 Baseline StartRoot 30 EndRoot
Option D
8

Which of the following is the graph of ?

Question illustration
A
On a coordinate plane, an absolute value curve opens up and to the right in quadrant 4. It starts at x = 3.
Option A
B
On a coordinate plane, an absolute value curve opens down and to the left in quadrants 1 and 2. It starts at x = 3.
Option B
C
On a coordinate plane, an absolute value curve opens down and to the left in quadrant 2. It starts at x = negative 3.
Option C
D
On a coordinate plane, an absolute value curve opens up and to the right in quadrants 3 and 4. It starts at x = negative 3.
Option D
9

What is the following product?

Question illustration
A
x squared (RootIndex 3 StartRoot 28 x squared EndRoot)
Option A
B
x Superscript 5 Baseline (RootIndex 3 StartRoot 28 x EndRoot)
Option B
C
4 x squared (RootIndex 3 StartRoot 3 x squared EndRoot)
Option C
D
4 x Superscript 5 Baseline (RootIndex 3 StartRoot 3 x EndRoot)
Option D
10

The formula gives the length of the side, s, of a cube with a surface area, SA. How much longer is the side of a cube with a surface area of 1,200 square inches than a cube with the surface area of 768 square inches?

Question illustration
A
in.
Option A
B
in.
Option B
C
in.
Option C
D
in.
Option D
11

What is the simplified form of the following expression?

Question illustration
A
6 StartRoot 2 EndRoot
Option A
B
18 StartRoot 2 EndRoot
Option B
C
30 StartRoot 2 EndRoot
Option C
D
36 StartRoot 2 EndRoot
Option D
12

What is the solution of ?

Question illustration
A
x = 142
B
x = 232
C
x = 322
D
no solution
13

What is the following product?

Question illustration
A
2 StartRoot 10 EndRoot
Option A
B
3 StartRoot 10 EndRoot
Option B
C
4 StartRoot 10 EndRoot
Option C
D
10 StartRoot 3 EndRoot
Option D
14

The orbital period, P, of a planet and the planet’s distance from the sun, a, in astronomical units is related by the formula . If Saturn’s orbital period is 29.5 years, what is its distance from the sun?

Question illustration
A
9.5 AU
B
19.7 AU
C
44.3 AU
D
160.2 AU
15

What is the following simplified product? Assume

Question illustration
A
10 x Superscript 4 Baseline StartRoot 6 EndRoot + x cubed StartRoot 30 x EndRoot minus 10 x Superscript 4 Baseline StartRoot 3 EndRoot + x squared StartRoot 15 x EndRoot
Option A
B
11 x Superscript 4 Baseline StartRoot 6 EndRoot + x cubed StartRoot 30 x EndRoot minus x Superscript 4 Baseline StartRoot 75 EndRoot + x squared StartRoot 15 EndRoot
Option B
C
10 x Superscript 4 Baseline StartRoot 6 EndRoot + x cubed StartRoot 30 x EndRoot minus 10 x Superscript 4 Baseline StartRoot 3 EndRoot minus x squared StartRoot 15 EndRoot
Option C
D
11 x Superscript 4 Baseline StartRoot 6 EndRoot + x cubed StartRoot 30 x EndRoot minus 10 x Superscript 4 Baseline StartRoot 3 EndRoot minus x cubed StartRoot 15 x EndRoot
Option D
16

What is the following sum?

Question illustration
A
7 x (RootIndex 6 StartRoot x squared y EndRoot)
Option A
B
7 x squared (RootIndex 6 StartRoot x y squared EndRoot)
Option B
C
7 x squared (RootIndex 3 StartRoot x y squared EndRoot)
Option C
D
7 x (RootIndex 3 StartRoot x squared y EndRoot)
Option D
17

If the range of and the range of are the same, which statement is true about the value of m?

Question illustration
A
m can only equal 1.
B
m can be any positive real number.
C
m can be any negative real number.
D
m can be any real number.
18

Which of the following describes the graph of compared to the parent cube root function?

Question illustration
A
stretched by a factor of 2 and translated 64 units right and 5 units down
B
stretched by a factor of 8 and translated 8 units right and 5 units down
C
stretched by a factor of 2 and translated 8 units right and 5 units down
D
stretched by a factor of 8 and translated 64 units right and 5 units down
19

Which expression is equivalent to ?

Question illustration
A
StartFraction RootIndex 4 StartRoot 200 EndRoot Over 2 EndFraction
Option A
B
StartFraction RootIndex 4 StartRoot 20 EndRoot Over 2 EndFraction
Option B
C
StartFraction 2 StartRoot 5 EndRoot Over 5 EndFraction
Option C
D
StartFraction 100 Over 8 EndFraction
Option D
20

What is the following quotient?

Question illustration
A
StartFraction StartRoot 3 EndRoot Over 4 EndFraction
Option A
B
StartFraction 1 + StartRoot 3 EndRoot Over 4 EndFraction
Option B
C
StartFraction 1 minus StartRoot 3 EndRoot Over 4 EndFraction
Option C
D
StartFraction negative 1 + StartRoot 3 EndRoot Over 2 EndFraction
Option D

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