Question 1

Multiply or divide.
-$\frac { \sqrt { - 70 } } { \sqrt { - 10 } }$

Accepted Answer

A)  $- \sqrt { 7 }$ 
B)  $i \sqrt { 7 }$ 
C)  $- \mathrm { i } \sqrt { 7 }$ 
D)  $\sqrt { 7 }$ 
A)  $- \sqrt { 7 }$ 
B)  $i \sqrt { 7 }$ 
C)  $- \mathrm { i } \sqrt { 7 }$ 
D)  $\sqrt { 7 }$

Question 2

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers.
-$\frac { \sqrt { 7 } - \sqrt { 8 } } { \sqrt { 7 } + \sqrt { 8 } }$

Accepted Answer

A)  $- 15 - 2 \sqrt { 56 }$ 
B)  $2 \sqrt { 56 } - 15$ 
C)  $15 - 2 \sqrt { 56 }$ 
D)  $15 + 2 \sqrt { 56 }$ 
A)  $- 15 - 2 \sqrt { 56 }$ 
B)  $2 \sqrt { 56 } - 15$ 
C)  $15 - 2 \sqrt { 56 }$ 
D)  $15 + 2 \sqrt { 56 }$

Question 3

Simplify the radical expression. Assume that all variables represent positive real numbers.
-$\sqrt { 6 }$

Accepted Answer

A)  2 
B)  $2 \sqrt { 3 }$ 
C)  $\sqrt { 6 }$ 
D)  $3 \sqrt { 2 }$ 
A)  2 
B)  $2 \sqrt { 3 }$ 
C)  $\sqrt { 6 }$ 
D)  $3 \sqrt { 2 }$

Question 4

Find the square root. Assume that all variables represent positive real numbers.
-$\sqrt { 0.09 }$

Accepted Answer

A)  $0.003$ 
B)  3 
C)  $0.3$ 
D)  $0.03$ 
A)  $0.003$ 
B)  3 
C)  $0.3$ 
D)  $0.03$

Question 5

Write in terms of i.
-$\sqrt { - 1600 }$

Accepted Answer

A)  $40 \mathrm { i }$ 
B)  $- 40 \mathrm { i }$ 
C)  $\mathrm { i } \sqrt { 40 }$ 
D)  $\pm 40$ 
A)  $40 \mathrm { i }$ 
B)  $- 40 \mathrm { i }$ 
C)  $\mathrm { i } \sqrt { 40 }$ 
D)  $\pm 40$

Question 6

Factor the given factor from the expression.
-$x ^ { 1 / 3 } ; x ^ { 13 / 3 } + x ^ { 1 / 3 }$

Accepted Answer

A)  $x ^ { 1 / 3 } \left( x ^ { 4 } + x \right)$ 
B)  $x ^ { 1 / 3 } \left( x ^ { 13 } + x \right)$ 
C)  $x ^ { 1 / 3 } \left( x ^ { 4 } + 1 \right)$ 
D)  $x ^ { 1 / 3 } \left( x ^ { 13 } + 1 \right)$ 
A)  $x ^ { 1 / 3 } \left( x ^ { 4 } + x \right)$ 
B)  $x ^ { 1 / 3 } \left( x ^ { 13 } + x \right)$ 
C)  $x ^ { 1 / 3 } \left( x ^ { 4 } + 1 \right)$ 
D)  $x ^ { 1 / 3 } \left( x ^ { 13 } + 1 \right)$

Question 7

Factor the given factor from the expression.
-$\mathrm { s } ^ { - 5 / 7 } ; 15 \mathrm {~s} ^ { 1 / 7 } - 3 \mathrm {~s} ^ { - 5 / 7 }$

Accepted Answer

A)  $s ^ { 1 / 7 } \left( 15 s ^ { 6 / 7 } - 3 ^ { 2 / 1 } \right)$ 
B)  $s ^ { - 5 / 7 } ( 15 s ^{6 / 7} - 3 s )$ 
C)  $s 1 / 3 \left( 15 - 3 s ^ { 2 / 1 } \right)$ 
D)  $ { s } ^ { - 5 / 7 } ( 15 \mathrm {~s}^{ 6 / 7} - 3 )$ 
A)  $s ^ { 1 / 7 } \left( 15 s ^ { 6 / 7 } - 3 ^ { 2 / 1 } \right)$ 
B)  $s ^ { - 5 / 7 } ( 15 s ^{6 / 7} - 3 s )$ 
C)  $s 1 / 3 \left( 15 - 3 s ^ { 2 / 1 } \right)$ 
D)  $ { s } ^ { - 5 / 7 } ( 15 \mathrm {~s}^{ 6 / 7} - 3 )$

Question 8

Solve the problem.
-The maximum distance $d$ in kilometers that you can see from a height $h$ in meters is given by the formula $\mathrm { d } = 3.5 \sqrt { \mathrm { h } }$. How high above the ground must you be to see 35 kilometers. (Round to the nearest tenth of a meter.)

Accepted Answer

A)  $100 \mathrm {~m}$ 
B)  $10 \mathrm {~m}$ 
C)  $350 \mathrm {~m}$ 
D)  $20.7 \mathrm {~m}$ 
A)  $100 \mathrm {~m}$ 
B)  $10 \mathrm {~m}$ 
C)  $350 \mathrm {~m}$ 
D)  $20.7 \mathrm {~m}$

Question 9

Multiply, and then simplify if possible. Assume all variables represent positive real numbers.
-$( \sqrt [ 3 ] { 9 } + 3 ) ( \sqrt [ 3 ] { 3 } - 1 )$

Accepted Answer

A)  0 
B)  $\sqrt [ 3 ] { 9 } - 3 \sqrt [ 3 ] { 3 }$ 
C)  $3 \sqrt [ 3 ] { 3 } + \sqrt [ 3 ] { 9 }$ 
D)  $3 \sqrt [ 3 ] { 3 } - \sqrt [ 3 ] { 9 }$ 
A)  0 
B)  $\sqrt [ 3 ] { 9 } - 3 \sqrt [ 3 ] { 3 }$ 
C)  $3 \sqrt [ 3 ] { 3 } + \sqrt [ 3 ] { 9 }$ 
D)  $3 \sqrt [ 3 ] { 3 } - \sqrt [ 3 ] { 9 }$

Question 10

Fill in the blank with one of the words or phrases listed below. $$\begin{array} { l l l } 
\text { index rationalizing } & \text { conjugate } & \text { principal square rootcube root midpoint } \
\text { complex numberlike radicals } & \text { radicand } & \text { imaginary unit } \quad \text { distance }
\end{array}$$
-In the natation   n is called the and a is called the ---------------

Accepted Answer

A)  index, conjugate 
B)  conjugate, radicand 
C)  index, radicand 
D)  radicand, index 
A)  index, conjugate 
B)  conjugate, radicand 
C)  index, radicand 
D)  radicand, index

Question 11

Use rational exponents to simplify the following.
-$\sqrt [ 16 ] { ( x + 7 ) ^ { 4 } }$

Accepted Answer

A)  $( x + 7 ) ^ { 1 / 4 }$ 
B)  $x ^ { 4 } + 7 ^ { 4 }$ 
C)  $( x + 7 ) ^ { 4 }$ 
D)  $x ^ { 1 / 4 } + 7 ^ { 1 / 4 }$ 
A)  $( x + 7 ) ^ { 1 / 4 }$ 
B)  $x ^ { 4 } + 7 ^ { 4 }$ 
C)  $( x + 7 ) ^ { 4 }$ 
D)  $x ^ { 1 / 4 } + 7 ^ { 1 / 4 }$

Question 12

Use the product rule to multiply. Assume all variables represent positive real numbers.
-$\sqrt { 3 x ^ { 3 } } \cdot \sqrt { 3 x ^ { 5 } }$

Accepted Answer

A)  $x^4 \sqrt { 6 }$ 
B)  $3 \mathrm { x } ^ { 4 }$ 
C)  $\sqrt { 9 x ^ { 8 } }$ 
D)  $\sqrt { 3 x ^ { 4 } }$ 
A)  $x^4 \sqrt { 6 }$ 
B)  $3 \mathrm { x } ^ { 4 }$ 
C)  $\sqrt { 9 x ^ { 8 } }$ 
D)  $\sqrt { 3 x ^ { 4 } }$

Question 13

Add or subtract. Assume all variables represent positive real numbers.
-$\sqrt { 112 } + \sqrt { 448 }$

Accepted Answer

A)  $- 4 \sqrt { 7 }$ 
B)  $12 \sqrt { 14 }$ 
C)  84 
D)  $12 \sqrt { 7 }$ 
A)  $- 4 \sqrt { 7 }$ 
B)  $12 \sqrt { 14 }$ 
C)  84 
D)  $12 \sqrt { 7 }$

Question 14

Solve.
-$\sqrt { 3 x + 5 } + 4 = 9$

Accepted Answer

A)  60 
B)  $\frac { 20 } { 3 }$ 
C)  $\frac { 3 } { 20 }$ 
D)  $\varnothing$ 
A)  60 
B)  $\frac { 20 } { 3 }$ 
C)  $\frac { 3 } { 20 }$ 
D)  $\varnothing$

Question 15

Find the midpoint of the line segment whose endpoints are given.
-$( - 8 , - 4 ) , ( 9 , - 5 )$

Accepted Answer

A)  $( - 17,1 )$ 
B)  $( 1 , - 9 )$ 
C)  $\left( \frac { 1 } { 2 } , - \frac { 9 } { 2 } \right)$ 
D)  $\left( - \frac { 17 } { 2 } , \frac { 1 } { 2 } \right)$ 
A)  $( - 17,1 )$ 
B)  $( 1 , - 9 )$ 
C)  $\left( \frac { 1 } { 2 } , - \frac { 9 } { 2 } \right)$ 
D)  $\left( - \frac { 17 } { 2 } , \frac { 1 } { 2 } \right)$

Question 16

Evaluate.
-If $f ( x ) = \sqrt { 2 x - 1 }$, find the value of $f ( 11 )$.

Accepted Answer

A)  21 
B)  22 
C)  $\sqrt { 21 }$ 
D)  $\sqrt { 22 }$ 
A)  21 
B)  22 
C)  $\sqrt { 21 }$ 
D)  $\sqrt { 22 }$

Question 17

Solve.
-$\sqrt { 5 x + 1 } + 8 = 0$

Accepted Answer

A)  $\frac { 5 } { 63 }$ 
B)  315 
C)  $\frac { 63 } { 5 }$ 
D)  $\varnothing$ 
A)  $\frac { 5 } { 63 }$ 
B)  315 
C)  $\frac { 63 } { 5 }$ 
D)  $\varnothing$

Question 18

Solve.
-Find the area of the trapezoid. Simplify if possible.

Accepted Answer

A)  $183 \sqrt { 7 }$ sq. $m$ 
B)  $1891 \sqrt { 35 }$ sq, m 
C)  $183 \sqrt { 35 }$ sq. $m$ 
D)  $366 \sqrt { 35 }$ sq. $\mathrm { m }$ 
A)  $183 \sqrt { 7 }$ sq. $m$ 
B)  $1891 \sqrt { 35 }$ sq, m 
C)  $183 \sqrt { 35 }$ sq. $m$ 
D)  $366 \sqrt { 35 }$ sq. $\mathrm { m }$

Question 19

Simplify the radical expression. Assume that all variables represent positive real numbers.
-$\frac { \sqrt { 63 x ^ { 11 } } } { \sqrt { 7 x } }$

Accepted Answer

A)  $3 x^{ 10}$ 
B)  $3 x ^ { 5 } \sqrt { 7 }$ 
C)  $3 \sqrt { \mathrm { x } ^ { 11 } }$ 
D)  $3 x ^ { 5 }$ 
A)  $3 x^{ 10}$ 
B)  $3 x ^ { 5 } \sqrt { 7 }$ 
C)  $3 \sqrt { \mathrm { x } ^ { 11 } }$ 
D)  $3 x ^ { 5 }$

Question 20

Use the product rule to multiply. Assume all variables represent positive real numbers.
-$\sqrt [ 4 ] { 16 } \cdot \sqrt [ 4 ] { 256 }$

Accepted Answer

A)  6 
B)  $- 8$ 
C)  $- 2$ 
D)  8 
A)  6 
B)  $- 8$ 
C)  $- 2$ 
D)  8

Multiply or divide. - $\frac { \sqrt { - 70 } } { \sqrt { - 10 } }$

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers. - $\frac { \sqrt { 7 } - \sqrt { 8 } } { \sqrt { 7 } + \sqrt { 8 } }$

Simplify the radical expression. Assume that all variables represent positive real numbers. - $\sqrt { 6 }$

Find the square root. Assume that all variables represent positive real numbers. - $\sqrt { 0.09 }$

Write in terms of i. - $\sqrt { - 1600 }$

Factor the given factor from the expression. - $x ^ { 1 / 3 } ; x ^ { 13 / 3 } + x ^ { 1 / 3 }$

Factor the given factor from the expression. - $\mathrm { s } ^ { - 5 / 7 } ; 15 \mathrm {~s} ^ { 1 / 7 } - 3 \mathrm {~s} ^ { - 5 / 7 }$

Solve the problem. -The maximum distance $d$ in kilometers that you can see from a height $h$ in meters is given by the formula $\mathrm { d } = 3.5 \sqrt { \mathrm { h } }$ . How high above the ground must you be to see 35 kilometers. (Round to the nearest tenth of a meter.)

Multiply, and then simplify if possible. Assume all variables represent positive real numbers. - $( \sqrt [ 3 ] { 9 } + 3 ) ( \sqrt [ 3 ] { 3 } - 1 )$

Use rational exponents to simplify the following. - $\sqrt [ 16 ] { ( x + 7 ) ^ { 4 } }$

Use the product rule to multiply. Assume all variables represent positive real numbers. - $\sqrt { 3 x ^ { 3 } } \cdot \sqrt { 3 x ^ { 5 } }$

Add or subtract. Assume all variables represent positive real numbers. - $\sqrt { 112 } + \sqrt { 448 }$

Solve. - $\sqrt { 3 x + 5 } + 4 = 9$

Find the midpoint of the line segment whose endpoints are given. - $( - 8 , - 4 ) , ( 9 , - 5 )$

Evaluate. -If $f ( x ) = \sqrt { 2 x - 1 }$ , find the value of $f ( 11 )$ .

Solve. - $\sqrt { 5 x + 1 } + 8 = 0$

Solve. -Find the area of the trapezoid. Simplify if possible.

Simplify the radical expression. Assume that all variables represent positive real numbers. - $\frac { \sqrt { 63 x ^ { 11 } } } { \sqrt { 7 x } }$

Use the product rule to multiply. Assume all variables represent positive real numbers. - $\sqrt [ 4 ] { 16 } \cdot \sqrt [ 4 ] { 256 }$

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Exponents and Polynomials

Factoring Polynomials

Rational Expressions

More on Functions and Graphs

Inequalities and Absolute Value

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 10: Rational Exponents, Radicals, and Complex Numbers

Multiply or divide. - −70−10\frac { \sqrt { - 70 } } { \sqrt { - 10 } }−10​−70​​

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers. - 7−87+8\frac { \sqrt { 7 } - \sqrt { 8 } } { \sqrt { 7 } + \sqrt { 8 } }7​+8​7​−8​​

Simplify the radical expression. Assume that all variables represent positive real numbers. - 6\sqrt { 6 }6​

Find the square root. Assume that all variables represent positive real numbers. - 0.09\sqrt { 0.09 }0.09​

Write in terms of i. - −1600\sqrt { - 1600 }−1600​

Factor the given factor from the expression. - x1/3;x13/3+x1/3x ^ { 1 / 3 } ; x ^ { 13 / 3 } + x ^ { 1 / 3 }x1/3;x13/3+x1/3

Factor the given factor from the expression. - s−5/7;15 s1/7−3 s−5/7\mathrm { s } ^ { - 5 / 7 } ; 15 \mathrm {~s} ^ { 1 / 7 } - 3 \mathrm {~s} ^ { - 5 / 7 }s−5/7;15 s1/7−3 s−5/7

Solve the problem. -The maximum distance ddd in kilometers that you can see from a height hhh in meters is given by the formula d=3.5h\mathrm { d } = 3.5 \sqrt { \mathrm { h } }d=3.5h​ . How high above the ground must you be to see 35 kilometers. (Round to the nearest tenth of a meter.)

Multiply, and then simplify if possible. Assume all variables represent positive real numbers. - (93+3)(33−1)( \sqrt [ 3 ] { 9 } + 3 ) ( \sqrt [ 3 ] { 3 } - 1 )(39​+3)(33​−1)

Fill in the blank with one of the words or phrases listed below. index rationalizing conjugate principal square rootcube root midpoint complex numberlike radicals radicand imaginary unit distance -In the natation n is called the and a is called the ---------------

Use rational exponents to simplify the following. - (x+7)416\sqrt [ 16 ] { ( x + 7 ) ^ { 4 } }16(x+7)4​

Use the product rule to multiply. Assume all variables represent positive real numbers. - 3x3⋅3x5\sqrt { 3 x ^ { 3 } } \cdot \sqrt { 3 x ^ { 5 } }3x3​⋅3x5​

Add or subtract. Assume all variables represent positive real numbers. - 112+448\sqrt { 112 } + \sqrt { 448 }112​+448​

Solve. - 3x+5+4=9\sqrt { 3 x + 5 } + 4 = 93x+5​+4=9

Find the midpoint of the line segment whose endpoints are given. - (−8,−4),(9,−5)( - 8 , - 4 ) , ( 9 , - 5 )(−8,−4),(9,−5)

Evaluate. -If f(x)=2x−1f ( x ) = \sqrt { 2 x - 1 }f(x)=2x−1​ , find the value of f(11)f ( 11 )f(11) .

Solve. - 5x+1+8=0\sqrt { 5 x + 1 } + 8 = 05x+1​+8=0