Question 1

Solve.
-$\sqrt { 3 x } = - 2$

Accepted Answer

A)  $- \frac { 2 } { 3 }$ 
B)  $\varnothing$ 
C)  $\frac { 4 } { 3 }$ 
D)  12 
A)  $- \frac { 2 } { 3 }$ 
B)  $\varnothing$ 
C)  $\frac { 4 } { 3 }$ 
D)  12

Question 2

Solve.
-When an object is dropped to the ground from a height of $h$ meters, the time it takes for the object to reach the ground is given by the equation $t = \sqrt { \frac { \mathrm { h } } { 4.9 } }$, where $t$ is measured in seconds. If an object hits the ground after falling for 5 seconds, find the height from which the object was dropped.

Accepted Answer

A)  $24.5 \mathrm {~m}$ 
B)  $1225 \mathrm {~m}$ 
C)  $245 \mathrm {~m}$ 
D)  $122.5 \mathrm {~m}$ 
A)  $24.5 \mathrm {~m}$ 
B)  $1225 \mathrm {~m}$ 
C)  $245 \mathrm {~m}$ 
D)  $122.5 \mathrm {~m}$

Question 3

Solve the problem.
-Rationalize the numerator of $\frac { \sqrt { 6 } + x } { 10 }$ and simplify.

Accepted Answer

A)  $\frac { 6 - x ^ { 2 } } { 10 ( \sqrt { 6 } - x ) }$ 
B)  $\frac { 6 - x ^ { 2 } } { 2 \sqrt { 15 } - 10 x }$ 
C)  $\frac { 6 + x ^ { 2 } } { 10 ( \sqrt { 6 } + x ) }$ 
D)  $10 ( \sqrt { 6 } + x )$ 
A)  $\frac { 6 - x ^ { 2 } } { 10 ( \sqrt { 6 } - x ) }$ 
B)  $\frac { 6 - x ^ { 2 } } { 2 \sqrt { 15 } - 10 x }$ 
C)  $\frac { 6 + x ^ { 2 } } { 10 ( \sqrt { 6 } + x ) }$ 
D)  $10 ( \sqrt { 6 } + x )$

Question 4

Use rational exponents to simplify the following.
-$\sqrt [ 4 ] { 16 x ^ { 2 } }$

Accepted Answer

A)  $16 \mathrm { x } ^ { 1 / 2 }$ 
B)  $2 x ^ { 1 / 2 }$ 
C)  $2 x ^ { 1 / 4 }$ 
D)  $2 x ^ { 2 }$ 
A)  $16 \mathrm { x } ^ { 1 / 2 }$ 
B)  $2 x ^ { 1 / 2 }$ 
C)  $2 x ^ { 1 / 4 }$ 
D)  $2 x ^ { 2 }$

Question 5

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers.
-$\frac { \sqrt { 3 } } { \sqrt { 7 } }$

Accepted Answer

A)  $\frac { \sqrt { 21 } } { 7 }$ 
B)  $\sqrt { 21 }$ 
C)  $\frac { \sqrt { 21 } } { 49 }$ 
D)  $\sqrt { 3 }$ 
A)  $\frac { \sqrt { 21 } } { 7 }$ 
B)  $\sqrt { 21 }$ 
C)  $\frac { \sqrt { 21 } } { 49 }$ 
D)  $\sqrt { 3 }$

Question 6

Find the root. Assume that all variables represent nonnegative real numbers.
-$- \sqrt [ 4 ] { 256 x ^ { 12 } y ^ { 8 } }$

Accepted Answer

A)  $6.233 x ^ { 3 } y ^ { 2 }$ 
B)  $16 \mathrm { x } ^ { 3 } \mathrm { y } ^ { 2 }$ 
C)  $- 4 x ^ { 3 } y ^ { 2 }$ 
D)  not a real number 
A)  $6.233 x ^ { 3 } y ^ { 2 }$ 
B)  $16 \mathrm { x } ^ { 3 } \mathrm { y } ^ { 2 }$ 
C)  $- 4 x ^ { 3 } y ^ { 2 }$ 
D)  not a real number

Question 7

Use rational exponents to simplify the following.
-$\sqrt [ 56 ] { x ^ { 8 } }$

Accepted Answer

A)  $x ^ { 7 }$ 
B)  $x ^ { 1 / 8 }$ 
C)  $x ^ { 1 / 56 }$ 
D)  $x ^ { 1 / 7 }$ 
A)  $x ^ { 7 }$ 
B)  $x ^ { 1 / 8 }$ 
C)  $x ^ { 1 / 56 }$ 
D)  $x ^ { 1 / 7 }$

Question 8

Find the square root. Assume that all variables represent positive real numbers.
-$- \sqrt { 25 }$

Accepted Answer

A)  not a real number 
B)  $- 12$ 
C)  $- 5$ 
D)  5 
A)  not a real number 
B)  $- 12$ 
C)  $- 5$ 
D)  5

Question 9

Find the midpoint of the line segment whose endpoints are given.
-$( - 4.1 , - 2.3 ) , ( 7.8,9.1 )$

Accepted Answer

A)  $( 1.85 , - 3.4 )$ 
B)  $( 1.85,3.4 )$ 
C)  $( - 5.95 , - 5.7 )$ 
D)  $( - 1.85,3.4 )$ 
A)  $( 1.85 , - 3.4 )$ 
B)  $( 1.85,3.4 )$ 
C)  $( - 5.95 , - 5.7 )$ 
D)  $( - 1.85,3.4 )$

Question 10

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

Accepted Answer

A)  $\frac { 16 } { 5 }$ 
B)  $\frac { 4 } { 5 }$ 
C)  20 
D)  80 
A)  $\frac { 16 } { 5 }$ 
B)  $\frac { 4 } { 5 }$ 
C)  20 
D)  80

Question 11

Simplify the radical expression. Assume that all variables represent positive real numbers.
-$\frac { \sqrt [ 3 ] { 20 } } { \sqrt [ 3 ] { 2 } }$

Accepted Answer

A)  $\frac { 1 } { \sqrt [ 3 ] { 10 } }$ 
B)  $\frac { 1 } { \sqrt [ 3 ] { 2 } }$ 
C)  $\sqrt [ 3 ] { 2 }$ 
D)  $\sqrt [ 3 ] { 10 }$ 
A)  $\frac { 1 } { \sqrt [ 3 ] { 10 } }$ 
B)  $\frac { 1 } { \sqrt [ 3 ] { 2 } }$ 
C)  $\sqrt [ 3 ] { 2 }$ 
D)  $\sqrt [ 3 ] { 10 }$

Question 12

Multiply or divide.
-$\frac { \sqrt { - 24 } } { \sqrt { - 2 } }$

Accepted Answer

A)  $2 \sqrt { 3 }$ 
B)  $- 2 \mathrm { i } \sqrt { 3 }$ 
C)  $- 2 \sqrt { 3 }$ 
D)  $2 \mathrm { i } \sqrt { 3 }$ 
A)  $2 \sqrt { 3 }$ 
B)  $- 2 \mathrm { i } \sqrt { 3 }$ 
C)  $- 2 \sqrt { 3 }$ 
D)  $2 \mathrm { i } \sqrt { 3 }$

Question 13

Find the power of i.
-$\mathrm {i } ^ { 9 }$

Accepted Answer

A)  -1 
B)  -i 
C)  i 
D)  1 
A)  -1 
B)  -i 
C)  i 
D)  1

Question 14

Multiply, and then simplify if possible. Assume all variables represent positive real numbers.
-$( \sqrt { 5 } + \sqrt { 11 } ) ( \sqrt { 5 } - \sqrt { 11 } )$

Accepted Answer

A)  $- 6$ 
B)  $5 - 2 \sqrt { 5 }$ 
C)  $5 - 2 \sqrt { 11 }$ 
D)  16 
A)  $- 6$ 
B)  $5 - 2 \sqrt { 5 }$ 
C)  $5 - 2 \sqrt { 11 }$ 
D)  16

Question 15

Write with positive exponents. Simplify if possible.
-$36 ^ { - 3 / 2 }$

Accepted Answer

A)  $\frac { 1 } { 216 }$ 
B)  216 
C)  $- \frac { 1 } { 216 }$ 
D)  $- 216$ 
A)  $\frac { 1 } { 216 }$ 
B)  216 
C)  $- \frac { 1 } { 216 }$ 
D)  $- 216$

Question 16

Perform the indicated operation. Write the result in the form a + bi.
-$\frac { 7 - 3 i } { 2 + i }$

Accepted Answer

A)  $\frac { 11 } { 5 } - \frac { 13 } { 5 } \mathrm { i }$ 
B)  $\frac { 17 } { 5 } - \frac { 1 } { 5 } \mathrm { i }$ 
C)  $\frac { 17 } { 5 } + \frac { 1 } { 5 } \mathrm { i }$ 
D)  $\frac { 11 } { 5 } + \frac { 13 } { 5 } \mathrm { i }$ 
A)  $\frac { 11 } { 5 } - \frac { 13 } { 5 } \mathrm { i }$ 
B)  $\frac { 17 } { 5 } - \frac { 1 } { 5 } \mathrm { i }$ 
C)  $\frac { 17 } { 5 } + \frac { 1 } { 5 } \mathrm { i }$ 
D)  $\frac { 11 } { 5 } + \frac { 13 } { 5 } \mathrm { i }$

Question 17

Perform the indicated operation. Write the result in the form a + bi.
-$( \sqrt { 7 } + 5 \mathrm { i } ) ( \sqrt { 7 } - 5 \mathrm { i } )$

Accepted Answer

A)  $7 - 2 i \sqrt { 5 }$ 
B)  $7 - 25 \mathrm { i }$ 
C)  $- 18 + 0 \mathrm { i }$ 
D)  $32 + 0 \mathrm { i }$ 
A)  $7 - 2 i \sqrt { 5 }$ 
B)  $7 - 25 \mathrm { i }$ 
C)  $- 18 + 0 \mathrm { i }$ 
D)  $32 + 0 \mathrm { i }$

Question 18

Find the midpoint of the line segment whose endpoints are given.
-$( 9,8 ) , ( 6,0 )$

Accepted Answer

A)  $\left( \frac { 3 } { 2 } , 4 \right)$ 
B)  $( 15,8 )$ 
C)  $( 3,8 )$ 
D)  $\left( \frac { 15 } { 2 } , 4 \right)$ 
A)  $\left( \frac { 3 } { 2 } , 4 \right)$ 
B)  $( 15,8 )$ 
C)  $( 3,8 )$ 
D)  $\left( \frac { 15 } { 2 } , 4 \right)$

Question 19

Solve.
-$\sqrt { 4 x + 4 } = \sqrt { 2 x + 1 } - 3$

Accepted Answer

A)  24 
B)  $\varnothing$ 
C)  0,24 
D)  0,4 
A)  24 
B)  $\varnothing$ 
C)  0,24 
D)  0,4

Question 20

Use rational exponents to write as a single radical expression.
-$\sqrt [ 9 ] { x } \cdot \sqrt [ 3 ] { x ^ { 2 } }$

Accepted Answer

A)  $\sqrt [ 9 ] { \mathrm { x } ^ { 3 } }$ 
B)  $x ^ { 21 }$ 
C)  $\sqrt [ 9 ] { x ^ { 7 } }$ 
D)  $\sqrt { \mathrm { x } ^ { 7 } }$ 
A)  $\sqrt [ 9 ] { \mathrm { x } ^ { 3 } }$ 
B)  $x ^ { 21 }$ 
C)  $\sqrt [ 9 ] { x ^ { 7 } }$ 
D)  $\sqrt { \mathrm { x } ^ { 7 } }$

Solve. - $\sqrt { 3 x } = - 2$

Solve the problem. -Rationalize the numerator of $\frac { \sqrt { 6 } + x } { 10 }$ and simplify.

Use rational exponents to simplify the following. - $\sqrt [ 4 ] { 16 x ^ { 2 } }$

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers. - $\frac { \sqrt { 3 } } { \sqrt { 7 } }$

Find the root. Assume that all variables represent nonnegative real numbers. - $- \sqrt [ 4 ] { 256 x ^ { 12 } y ^ { 8 } }$

Use rational exponents to simplify the following. - $\sqrt [ 56 ] { x ^ { 8 } }$

Find the square root. Assume that all variables represent positive real numbers. - $- \sqrt { 25 }$

Find the midpoint of the line segment whose endpoints are given. - $( - 4.1 , - 2.3 ) , ( 7.8,9.1 )$

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

Simplify the radical expression. Assume that all variables represent positive real numbers. - $\frac { \sqrt [ 3 ] { 20 } } { \sqrt [ 3 ] { 2 } }$

Multiply or divide. - $\frac { \sqrt { - 24 } } { \sqrt { - 2 } }$

Find the power of i. - $\mathrm {i } ^ { 9 }$

Multiply, and then simplify if possible. Assume all variables represent positive real numbers. - $( \sqrt { 5 } + \sqrt { 11 } ) ( \sqrt { 5 } - \sqrt { 11 } )$

Write with positive exponents. Simplify if possible. - $36 ^ { - 3 / 2 }$

Perform the indicated operation. Write the result in the form a + bi. - $\frac { 7 - 3 i } { 2 + i }$

Perform the indicated operation. Write the result in the form a + bi. - $( \sqrt { 7 } + 5 \mathrm { i } ) ( \sqrt { 7 } - 5 \mathrm { i } )$

Find the midpoint of the line segment whose endpoints are given. - $( 9,8 ) , ( 6,0 )$

Solve. - $\sqrt { 4 x + 4 } = \sqrt { 2 x + 1 } - 3$

Use rational exponents to write as a single radical expression. - $\sqrt [ 9 ] { x } \cdot \sqrt [ 3 ] { x ^ { 2 } }$

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

Solve. - 3x=−2\sqrt { 3 x } = - 23x​=−2

Solve the problem. -Rationalize the numerator of 6+x10\frac { \sqrt { 6 } + x } { 10 }106​+x​ and simplify.

Use rational exponents to simplify the following. - 16x24\sqrt [ 4 ] { 16 x ^ { 2 } }416x2​

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers. - 37\frac { \sqrt { 3 } } { \sqrt { 7 } }7​3​​

Find the root. Assume that all variables represent nonnegative real numbers. - −256x12y84- \sqrt [ 4 ] { 256 x ^ { 12 } y ^ { 8 } }−4256x12y8​

Use rational exponents to simplify the following. - x856\sqrt [ 56 ] { x ^ { 8 } }56x8​

Find the square root. Assume that all variables represent positive real numbers. - −25- \sqrt { 25 }−25​

Find the midpoint of the line segment whose endpoints are given. - (−4.1,−2.3),(7.8,9.1)( - 4.1 , - 2.3 ) , ( 7.8,9.1 )(−4.1,−2.3),(7.8,9.1)

Solve. - 5x=4\sqrt { 5 x } = 45x​=4

Simplify the radical expression. Assume that all variables represent positive real numbers. - 20323\frac { \sqrt [ 3 ] { 20 } } { \sqrt [ 3 ] { 2 } }32​320​​

Multiply or divide. - −24−2\frac { \sqrt { - 24 } } { \sqrt { - 2 } }−2​−24​​

Find the power of i. - i9\mathrm {i } ^ { 9 }i9

Multiply, and then simplify if possible. Assume all variables represent positive real numbers. - (5+11)(5−11)( \sqrt { 5 } + \sqrt { 11 } ) ( \sqrt { 5 } - \sqrt { 11 } )(5​+11​)(5​−11​)

Write with positive exponents. Simplify if possible. - 36−3/236 ^ { - 3 / 2 }36−3/2

Perform the indicated operation. Write the result in the form a + bi. - 7−3i2+i\frac { 7 - 3 i } { 2 + i }2+i7−3i​

Perform the indicated operation. Write the result in the form a + bi. - (7+5i)(7−5i)( \sqrt { 7 } + 5 \mathrm { i } ) ( \sqrt { 7 } - 5 \mathrm { i } )(7​+5i)(7​−5i)

Find the midpoint of the line segment whose endpoints are given. - (9,8),(6,0)( 9,8 ) , ( 6,0 )(9,8),(6,0)

Solve. - 4x+4=2x+1−3\sqrt { 4 x + 4 } = \sqrt { 2 x + 1 } - 34x+4​=2x+1​−3

Use rational exponents to write as a single radical expression. - x9⋅x23\sqrt [ 9 ] { x } \cdot \sqrt [ 3 ] { x ^ { 2 } }9x​⋅3x2​