Question 1

Rationalize the denominator. $\frac { - 13 } { \sqrt { x } }$

Accepted Answer

A)  $\frac { - 13 \sqrt { x } } { x }$ 
B)  $\frac { 169 } { x }$ 
C)  $\frac { x \sqrt { x } } { - 13 }$ 
D)  Already rationalized. 
A)  $\frac { - 13 \sqrt { x } } { x }$ 
B)  $\frac { 169 } { x }$ 
C)  $\frac { x \sqrt { x } } { - 13 }$ 
D)  Already rationalized.

Question 2

The multiplication property of radicals indicates that if n a and n b are real numbers, then $\sqrt [ n ] { a b } =$_____

Accepted Answer

A)  $\sqrt { a } \cdot \sqrt { b }$ 
B)  $\frac { \sqrt [ n ] { a } } { n - }$ 
C)  $\sqrt [ n ] { a ^ { b } }$ 
D)  $\sqrt [ n ] { a } \cdot \sqrt [ n ] { b }$ b 
A)  $\sqrt { a } \cdot \sqrt { b }$ 
B)  $\frac { \sqrt [ n ] { a } } { n - }$ 
C)  $\sqrt [ n ] { a ^ { b } }$ 
D)  $\sqrt [ n ] { a } \cdot \sqrt [ n ] { b }$ b

Question 3

Multiply the radical expressions. $( 9 - \sqrt { 11 } ) ^ { 2 }$

Accepted Answer

A)  $92 - 18 \sqrt { 11 }$ 
B)  $- 40$ 
C)  $70 - 18 \sqrt { 11 }$ 
D)  70 
A)  $92 - 18 \sqrt { 11 }$ 
B)  $- 40$ 
C)  $70 - 18 \sqrt { 11 }$ 
D)  70

Question 4

Write the expression by using rational exponents rather than radical notation. $\sqrt [ 3 ] { x }$

Accepted Answer

A)  $x ^ { - 3 }$ 
B)  $\frac { \sqrt { x } } { 3 }$ 
C)  $x ^ { 3 }$ 
D)  $x ^ { 1 / 3 }$ 
A)  $x ^ { - 3 }$ 
B)  $\frac { \sqrt { x } } { 3 }$ 
C)  $x ^ { 3 }$ 
D)  $x ^ { 1 / 3 }$

Question 5

Simplify the radical expression.
$\sqrt { x ^ { 2 } y ^ { 4 } }$

Accepted Answer

A)  $| x | y ^ { 2 }$ 
B)  $\left| x y ^ { 3 } \right|$ 
C)  $x y ^ { 2 }$ 
D)  $x y ^ { 3 }$ 
A)  $| x | y ^ { 2 }$ 
B)  $\left| x y ^ { 3 } \right|$ 
C)  $x y ^ { 2 }$ 
D)  $x y ^ { 3 }$

Question 6

Simplify the expression. $\sqrt { - 72 }$

Accepted Answer

A)  $- 6 i \sqrt { 2 }$ 
B)  $6 \sqrt { 2 i }$ 
C)  $6 i \sqrt { 2 }$ 
D)  $36 i \sqrt { 2 }$ 
A)  $- 6 i \sqrt { 2 }$ 
B)  $6 \sqrt { 2 i }$ 
C)  $6 i \sqrt { 2 }$ 
D)  $36 i \sqrt { 2 }$

Question 7

Simplify using the division property of radicals. Assume that all variables represent positive real numbers. $$\sqrt [ 3 ] { \frac { 88 m ^ { 23 } n ^ { 2 } } { m n ^ { 20 } } }$$

Accepted Answer

The answer of Simplify using the division property of radicals....

Question 8

The amount of time it takes an object dropped from an initial height of h0 feet to reach a height of h feet is given by the formula $t = \sqrt { \frac { h _ { 0 } - h } { 16 } }$ How long would it take an object to reach the ground from the top of a building that is 430 feet tall? Round to the nearest tenth of a second.

Accepted Answer

The answer of The amount of time it takes an...

Question 9

The amount of time it takes an object dropped from an initial height of h0 feet to reach a height of h feet is given by the formula $t = \sqrt { \frac { h _ { 0 } - h } { 16 } }$ If it takes an object dropped from the top of the Empire State Building in New York 6.6 seconds to land on top Of an adjacent building that is 550 feet tall, approximate the height of the Empire State Building to the Nearest foot.

Accepted Answer

A)  1,150 feet 
B)  1,247 feet 
C)  1,120 feet 
D)  1,020 feet 
A)  1,150 feet 
B)  1,247 feet 
C)  1,120 feet 
D)  1,020 feet

Question 10

Simplify the radical expression.
$\sqrt { ( - 14 - 8 x ) ^ { 2 } }$

Accepted Answer

A)  $196 - 64 x$ 
B)  $| - 14 - 8 x |$ 
C)  $- 14 - 8 x$ 
D)  $14 + 8 x$ 
A)  $196 - 64 x$ 
B)  $| - 14 - 8 x |$ 
C)  $- 14 - 8 x$ 
D)  $14 + 8 x$

Question 11

Solve the radical equation, if possible. $$\sqrt { 4 x - 8 } = \sqrt { - 13 + 6 x }$$

Accepted Answer

The answer of Solve the radical equation, if possible. \[\sqrt...

Question 12

Identify the real and imaginary parts of the complex number. -7 + 8i

Accepted Answer

A)  Real: -7; imaginary: 8i 
B)  Real: -7; imaginary: 8 
C)  Real: 1; imaginary: i 
D)  Real: 8; imaginary: -7 
A)  Real: -7; imaginary: 8i 
B)  Real: -7; imaginary: 8 
C)  Real: 1; imaginary: i 
D)  Real: 8; imaginary: -7

Question 13

Convert the expression to radical notation. $16 z ^ { 4 / 7 }$

Accepted Answer

A)  $\sqrt [ 7 ] { ( 16 z ) ^ { 4 } }$ 
B)  $\sqrt [ 7 ] { 16 z ^ { 4 } }$ 
C)  $16 \sqrt [ 7 ] { z ^ { 4 } }$ 
D)  $16 \sqrt [ 4 ] { z ^ { 7 } }$ 
A)  $\sqrt [ 7 ] { ( 16 z ) ^ { 4 } }$ 
B)  $\sqrt [ 7 ] { 16 z ^ { 4 } }$ 
C)  $16 \sqrt [ 7 ] { z ^ { 4 } }$ 
D)  $16 \sqrt [ 4 ] { z ^ { 7 } }$

Question 14

Write the domain of the function in interval notation. $$g ( y ) = \sqrt [ 4 ] { 6 y - 24 }$$

Accepted Answer

A)  $[ 4 , \infty )$ 
B)  $( - \infty , \infty )$ 
C)  $( 4 , \infty )$ 
D)  $( - \infty , 4 ]$ 
A)  $[ 4 , \infty )$ 
B)  $( - \infty , \infty )$ 
C)  $( 4 , \infty )$ 
D)  $( - \infty , 4 ]$

Question 15

Solve the radical equation, if possible. $$\sqrt [ 5 ] { 8 z + 3 } = \sqrt [ 5 ] { 5 z + 12 }$$

Accepted Answer

A)  $\{ 3 \}$ 
B)  $\{ - 3 \}$ 
C)  $\{ 6 \}$ 
D)  $\{ 0 \}$ 
A)  $\{ 3 \}$ 
B)  $\{ - 3 \}$ 
C)  $\{ 6 \}$ 
D)  $\{ 0 \}$

Question 16

How high up a vertical wall will a 26 foot long extension ladder reach if its base is placed 10 feet away from the wall?

Accepted Answer

The answer of How high up a vertical wall will...

Question 17

Simplify the expression by using the properties of rational exponents. Write the final answer using positive exponents only. $$\left( \frac { t ^ { 4 } } { t ^ { - 6 } } \right) ^ { 1 / 2 }$$

Accepted Answer

A)  $t ^ { 8 }$ 
B)  $t ^ { 5 }$ 
C)  $t ^ { - 4 }$ 
D)  $t ^ { - 1 }$ 
A)  $t ^ { 8 }$ 
B)  $t ^ { 5 }$ 
C)  $t ^ { - 4 }$ 
D)  $t ^ { - 1 }$

Question 18

Multiply the radicals with different indices. Write the answer in radical form and simplify. $$\sqrt [ 3 ] { x y } \cdot \sqrt [ 5 ] { x y }$$

Accepted Answer

A)  $\sqrt [ 15 ] { x ^ { 2 } y ^ { 2 } }$ 
B)  $\sqrt [ 8 ] { x y }$ 
C)  $\sqrt [ 15 ] { ( x y ) ^ { 8 } }$ 
D)  $\sqrt [ 15 ] { x y }$ 
A)  $\sqrt [ 15 ] { x ^ { 2 } y ^ { 2 } }$ 
B)  $\sqrt [ 8 ] { x y }$ 
C)  $\sqrt [ 15 ] { ( x y ) ^ { 8 } }$ 
D)  $\sqrt [ 15 ] { x y }$

Question 19

Add or subtract the radical expressions as indicated, if possible. $3 m \sqrt { 125 m ^ { 2 } } + m ^ { 2 } \sqrt { 180 }$

Accepted Answer

A)  $21 \mathrm {~m} ^ { 2 } \sqrt { 5 }$ 
B)  $111 \mathrm {~m} ^ { 2 } \sqrt { 5 }$ 
C)  $111 \mathrm {~m} \sqrt { 5 }$ 
D)  Cannot be simplified further 
A)  $21 \mathrm {~m} ^ { 2 } \sqrt { 5 }$ 
B)  $111 \mathrm {~m} ^ { 2 } \sqrt { 5 }$ 
C)  $111 \mathrm {~m} \sqrt { 5 }$ 
D)  Cannot be simplified further

Question 20

Simplify the radical. Assume that all variables represent positive real numbers. $\sqrt [ 3 ] { 96 y ^ { 23 } }$

Accepted Answer

A)  $2 y \sqrt [ 3 ] { 12 y ^ { 20 } }$ 
B)  $2 y ^ { 7 } \sqrt [ 3 ] { 12 y ^ { 2 } }$ 
C)  $8 y ^ { 21 } \sqrt [ 3 ] { 12 y ^ { 2 } }$ 
D)  $y ^ { 7 } \sqrt [ 3 ] { 96 y ^ { 2 } }$ 
A)  $2 y \sqrt [ 3 ] { 12 y ^ { 20 } }$ 
B)  $2 y ^ { 7 } \sqrt [ 3 ] { 12 y ^ { 2 } }$ 
C)  $8 y ^ { 21 } \sqrt [ 3 ] { 12 y ^ { 2 } }$ 
D)  $y ^ { 7 } \sqrt [ 3 ] { 96 y ^ { 2 } }$

Rationalize the denominator. $\frac { - 13 } { \sqrt { x } }$

The multiplication property of radicals indicates that if n a and n b are real numbers, then $\sqrt [ n ] { a b } =$ _____

Multiply the radical expressions. $( 9 - \sqrt { 11 } ) ^ { 2 }$

Write the expression by using rational exponents rather than radical notation. $\sqrt [ 3 ] { x }$

Simplify the radical expression. $\sqrt { x ^ { 2 } y ^ { 4 } }$

Simplify the expression. $\sqrt { - 72 }$

Simplify using the division property of radicals. Assume that all variables represent positive real numbers. $\sqrt [ 3 ] { \frac { 88 m ^ { 23 } n ^ { 2 } } { m n ^ { 20 } } }$

Simplify the radical expression. $\sqrt { ( - 14 - 8 x ) ^ { 2 } }$

Solve the radical equation, if possible. $\sqrt { 4 x - 8 } = \sqrt { - 13 + 6 x }$

Identify the real and imaginary parts of the complex number. -7 + 8i

Convert the expression to radical notation. $16 z ^ { 4 / 7 }$

Write the domain of the function in interval notation. $g ( y ) = \sqrt [ 4 ] { 6 y - 24 }$

Solve the radical equation, if possible. $\sqrt [ 5 ] { 8 z + 3 } = \sqrt [ 5 ] { 5 z + 12 }$

How high up a vertical wall will a 26 foot long extension ladder reach if its base is placed 10 feet away from the wall?

Simplify the expression by using the properties of rational exponents. Write the final answer using positive exponents only. $\left( \frac { t ^ { 4 } } { t ^ { - 6 } } \right) ^ { 1 / 2 }$

Multiply the radicals with different indices. Write the answer in radical form and simplify. $\sqrt [ 3 ] { x y } \cdot \sqrt [ 5 ] { x y }$

Add or subtract the radical expressions as indicated, if possible. $3 m \sqrt { 125 m ^ { 2 } } + m ^ { 2 } \sqrt { 180 }$

Simplify the radical. Assume that all variables represent positive real numbers. $\sqrt [ 3 ] { 96 y ^ { 23 } }$

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables and Functions

Systems of Linear Equations and Inequalities

Polynomials

Rational Expressions and Rational Equations

Quadratic Equations, Functions and Inequalities

Exponential and Logarithmic Functions and Applications

Conic Sections

Binomial Expansions, Sequences, and Series

Online: Transformations, Piecewise-Defined Functions, and Probability

Filters

Exam 6: Radicals and Complex Numbers

Rationalize the denominator. −13x\frac { - 13 } { \sqrt { x } }x​−13​

The multiplication property of radicals indicates that if n a and n b are real numbers, then abn=\sqrt [ n ] { a b } =nab​= _____

Multiply the radical expressions. (9−11)2( 9 - \sqrt { 11 } ) ^ { 2 }(9−11​)2

Write the expression by using rational exponents rather than radical notation. x3\sqrt [ 3 ] { x }3x​

Simplify the radical expression. x2y4\sqrt { x ^ { 2 } y ^ { 4 } }x2y4​

Simplify the expression. −72\sqrt { - 72 }−72​

Simplify using the division property of radicals. Assume that all variables represent positive real numbers. 88m23n2mn203\sqrt [ 3 ] { \frac { 88 m ^ { 23 } n ^ { 2 } } { m n ^ { 20 } } }3mn2088m23n2​​

Simplify the radical expression. (−14−8x)2\sqrt { ( - 14 - 8 x ) ^ { 2 } }(−14−8x)2​

Solve the radical equation, if possible. 4x−8=−13+6x\sqrt { 4 x - 8 } = \sqrt { - 13 + 6 x }4x−8​=−13+6x​

Identify the real and imaginary parts of the complex number. -7 + 8i

Convert the expression to radical notation. 16z4/716 z ^ { 4 / 7 }16z4/7

Write the domain of the function in interval notation. g(y)=6y−244g ( y ) = \sqrt [ 4 ] { 6 y - 24 }g(y)=46y−24​

Solve the radical equation, if possible. 8z+35=5z+125\sqrt [ 5 ] { 8 z + 3 } = \sqrt [ 5 ] { 5 z + 12 }58z+3​=55z+12​

How high up a vertical wall will a 26 foot long extension ladder reach if its base is placed 10 feet away from the wall?

Simplify the expression by using the properties of rational exponents. Write the final answer using positive exponents only. (t4t−6)1/2\left( \frac { t ^ { 4 } } { t ^ { - 6 } } \right) ^ { 1 / 2 }(t−6t4​)1/2

Multiply the radicals with different indices. Write the answer in radical form and simplify. xy3⋅xy5\sqrt [ 3 ] { x y } \cdot \sqrt [ 5 ] { x y }3xy​⋅5xy​

Add or subtract the radical expressions as indicated, if possible. 3m125m2+m21803 m \sqrt { 125 m ^ { 2 } } + m ^ { 2 } \sqrt { 180 }3m125m2​+m2180​

Simplify the radical. Assume that all variables represent positive real numbers. 96y233\sqrt [ 3 ] { 96 y ^ { 23 } }396y23​

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables and Functions

Systems of Linear Equations and Inequalities

Polynomials

Rational Expressions and Rational Equations

Quadratic Equations, Functions and Inequalities

Exponential and Logarithmic Functions and Applications

Conic Sections

Binomial Expansions, Sequences, and Series

Online: Transformations, Piecewise-Defined Functions, and Probability

Filters

Rationalize the denominator. $\frac { - 13 } { \sqrt { x } }$

The multiplication property of radicals indicates that if n a and n b are real numbers, then $\sqrt [ n ] { a b } =$ _____

Multiply the radical expressions. $( 9 - \sqrt { 11 } ) ^ { 2 }$

Write the expression by using rational exponents rather than radical notation. $\sqrt [ 3 ] { x }$

Simplify the radical expression. $\sqrt { x ^ { 2 } y ^ { 4 } }$

Simplify the expression. $\sqrt { - 72 }$

Simplify using the division property of radicals. Assume that all variables represent positive real numbers. $\sqrt [ 3 ] { \frac { 88 m ^ { 23 } n ^ { 2 } } { m n ^ { 20 } } }$

Simplify the radical expression. $\sqrt { ( - 14 - 8 x ) ^ { 2 } }$

Solve the radical equation, if possible. $\sqrt { 4 x - 8 } = \sqrt { - 13 + 6 x }$

Convert the expression to radical notation. $16 z ^ { 4 / 7 }$

Write the domain of the function in interval notation. $g ( y ) = \sqrt [ 4 ] { 6 y - 24 }$

Solve the radical equation, if possible. $\sqrt [ 5 ] { 8 z + 3 } = \sqrt [ 5 ] { 5 z + 12 }$

Simplify the expression by using the properties of rational exponents. Write the final answer using positive exponents only. $\left( \frac { t ^ { 4 } } { t ^ { - 6 } } \right) ^ { 1 / 2 }$

Multiply the radicals with different indices. Write the answer in radical form and simplify. $\sqrt [ 3 ] { x y } \cdot \sqrt [ 5 ] { x y }$

Add or subtract the radical expressions as indicated, if possible. $3 m \sqrt { 125 m ^ { 2 } } + m ^ { 2 } \sqrt { 180 }$

Simplify the radical. Assume that all variables represent positive real numbers. $\sqrt [ 3 ] { 96 y ^ { 23 } }$