Question 1

Simplify the expression. $\frac { \sqrt { - 4 } } { \sqrt { 121 } }$

Accepted Answer

A)  $\frac { - \sqrt { 2 } } { 11 }$ 
B)  $- \frac { 2 } { 11 }$ 
C)  $\frac { 2 } { 11 } i$ 
D)  $\frac { 2 } { 11 }$ 
A)  $\frac { - \sqrt { 2 } } { 11 }$ 
B)  $- \frac { 2 } { 11 }$ 
C)  $\frac { 2 } { 11 } i$ 
D)  $\frac { 2 } { 11 }$

Question 2

Rationalize the denominator. $$\frac { 7 + \sqrt { 50 y } } { \sqrt { 8 } - 5 }$$

Accepted Answer

A)  $\frac { - 20 \sqrt { y } - 35 - 14 \sqrt { 2 } - 25 \sqrt { 2 y } } { 17 }$ 
B)  $\frac { 7 \sqrt { 8 } + 20 y } { 3 }$ 
C)  $\frac { 14 \sqrt { 2 } + 20 y - 35 - 25 \sqrt { 2 y } } { 33 }$ 
D)  $\frac { 7 + 5 \sqrt { 2 y } } { 2 \sqrt { 2 } - 5 }$ 
A)  $\frac { - 20 \sqrt { y } - 35 - 14 \sqrt { 2 } - 25 \sqrt { 2 y } } { 17 }$ 
B)  $\frac { 7 \sqrt { 8 } + 20 y } { 3 }$ 
C)  $\frac { 14 \sqrt { 2 } + 20 y - 35 - 25 \sqrt { 2 y } } { 33 }$ 
D)  $\frac { 7 + 5 \sqrt { 2 y } } { 2 \sqrt { 2 } - 5 }$

Question 3

Use a calculator to approximate the expression. Round to four decimal places, if necessary. $$\sqrt { 6 ^ { 3 } }$$

Accepted Answer

A)  108 
B)  3.3019 
C)  14.6969 
D)  1.8171 
A)  108 
B)  3.3019 
C)  14.6969 
D)  1.8171

Question 4

A creative group of students produces a reality television show that features various aspects of college and dorm life. Once the show begins airing on the university's public access cable channel, the function $w ( x ) = ( x + 125 ) ^ { 1 / 3 }$ represents the number of weeks that pass until x percent of the campus is watching the show. Compute w(50) to one decimal place, and interpret the result in the context of this problem.

Accepted Answer

w(50) = 5.6. It will

Question 5

Multiply the radical expressions. $- 5 \sqrt { y } ( \sqrt { y } + 10 )$

Accepted Answer

A)  $- 55 \sqrt { y }$ 
B)  $- 5 y + 10$ 
C)  $- 5 y ^ { 2 } - 50 \sqrt { y }$ 
D)  $- 5 y - 50 \sqrt { y }$ 
A)  $- 55 \sqrt { y }$ 
B)  $- 5 y + 10$ 
C)  $- 5 y ^ { 2 } - 50 \sqrt { y }$ 
D)  $- 5 y - 50 \sqrt { y }$

Question 6

Simplify the radical. $\sqrt [ 3 ] { 72 }$

Accepted Answer

A)  $8 \sqrt [ 3 ] { 36 }$ 
B)  $6 \sqrt [ 3 ] { 2 }$ 
C)  $8 \sqrt [ 3 ] { 9 }$ 
D)  $2 \sqrt [ 3 ] { 9 }$ 
A)  $8 \sqrt [ 3 ] { 36 }$ 
B)  $6 \sqrt [ 3 ] { 2 }$ 
C)  $8 \sqrt [ 3 ] { 9 }$ 
D)  $2 \sqrt [ 3 ] { 9 }$

Question 7

Simplify the complex number. Write the answer in the form a + bi. 
$\frac { - 12 + \sqrt { - 8 } } { 2 }$

Accepted Answer

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

Question 8

Rationalize the denominator. $\frac { 3 } { 9 - \sqrt { 5 } }$

Accepted Answer

A)  $\frac { 27 + 3 \sqrt { 5 } } { 56 }$ 
B)  $\frac { 3 } { 9 + \sqrt { 5 } }$ 
C)  $\frac { 27 + 3 \sqrt { 5 } } { 76 }$ 
D)  $\frac { 3 \sqrt { 5 } } { 4 }$ 
A)  $\frac { 27 + 3 \sqrt { 5 } } { 56 }$ 
B)  $\frac { 3 } { 9 + \sqrt { 5 } }$ 
C)  $\frac { 27 + 3 \sqrt { 5 } } { 76 }$ 
D)  $\frac { 3 \sqrt { 5 } } { 4 }$

Question 9

Write the domain of the function in interval notation. $$f ( x ) = \sqrt [ 3 ] { x - 12 }$$

Accepted Answer

A)  $[ 12 , \infty )$ 
B)  $( 12 , \infty )$ 
C)  $( - \infty , 12 ]$ 
D)  $( - \infty , \infty )$ 
A)  $[ 12 , \infty )$ 
B)  $( 12 , \infty )$ 
C)  $( - \infty , 12 ]$ 
D)  $( - \infty , \infty )$

Question 10

Convert the expression to radical form and simplify. $$( - 64 ) ^ { 1 / 3 }$$

Accepted Answer

A)  $- \frac { 1 } { 4 }$ 
B)  $- 4$ 
C)  4 
D)  $- \frac { 64 } { 3 }$ 
A)  $- \frac { 1 } { 4 }$ 
B)  $- 4$ 
C)  4 
D)  $- \frac { 64 } { 3 }$

Question 11

Solve the radical equation, if possible. $$\sqrt { 2 x - 8 } = \sqrt { 11 + 4 x }$$

Accepted Answer

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

Question 12

Find the length of the third side of the triangle by using the Pythagorean theorem.

Accepted Answer

A)  10 in. 
B)  12 in. 
C)  14 in. 
D)  28 in. 
A)  10 in. 
B)  12 in. 
C)  14 in. 
D)  28 in.

Question 13

Simplify the expression. $$\frac { \sqrt { - 100 } } { \sqrt { - 25 } }$$

Accepted Answer

The answer of Simplify the expression. \[\frac { \sqrt {...

Question 14

Simplify the radical. $\sqrt { 30 }$

Accepted Answer

A)  $3 \sqrt { 10 }$ 
B)  $4 \sqrt { 7 }$ 
C)  $2 \sqrt { 15 }$ 
D)  Cannot be simplified 
A)  $3 \sqrt { 10 }$ 
B)  $4 \sqrt { 7 }$ 
C)  $2 \sqrt { 15 }$ 
D)  Cannot be simplified

Question 15

Simplify the expression by using the properties of rational exponents. Write the final answer using positive exponents only. 
$\left( a ^ { 1 / 5 } a ^ { 1 / 6 } \right) ^ { 30 }$

Accepted Answer

A)  $a ^ { 11 }$ 
B)  $a ^ { 2 }$ 
C)  $30 a ^ { 11 / 30 }$ 
D)  $30 a ^ { 2 }$ 
A)  $a ^ { 11 }$ 
B)  $a ^ { 2 }$ 
C)  $30 a ^ { 11 / 30 }$ 
D)  $30 a ^ { 2 }$

Question 16

Add or subtract the radical expressions as indicated, if possible. $$z ^ { 2 } \sqrt { 18 z } + 7 \sqrt { 200 z }$$

Accepted Answer

A)  $\left( 3 z ^ { 2 } + 70 \right) \sqrt { 2 z }$ 
B)  $\left( 18 z ^ { 2 } + 1400 \right) \sqrt { z }$ 
C)  $\left( z ^ { 2 } + 7 \right) \sqrt { 218 z }$ 
D)  Cannot be simplified further 
A)  $\left( 3 z ^ { 2 } + 70 \right) \sqrt { 2 z }$ 
B)  $\left( 18 z ^ { 2 } + 1400 \right) \sqrt { z }$ 
C)  $\left( z ^ { 2 } + 7 \right) \sqrt { 218 z }$ 
D)  Cannot be simplified further

Question 17

Simplify the radical. $\sqrt { 140 }$

Accepted Answer

A)  $4 \sqrt { 35 }$ 
B)  $2 \sqrt { 70 }$ 
C)  $2 \sqrt { 35 }$ 
D)  Cannot be simplified 
A)  $4 \sqrt { 35 }$ 
B)  $2 \sqrt { 70 }$ 
C)  $2 \sqrt { 35 }$ 
D)  Cannot be simplified

Question 18

Evaluate the root without using a calculator or note that root is not a real number. 
$- \sqrt { 0.49 }$

Accepted Answer

A)  $0.7$ 
B)  $0.2401$ 
C)  $- 0.7$ 
D)  Not a real number 
A)  $0.7$ 
B)  $0.2401$ 
C)  $- 0.7$ 
D)  Not a real number

Question 19

Multiply the radicals with different indices. Write the answer in radical form and simplify. $$\sqrt [ 3 ] { z ^ { 5 } } \cdot \sqrt [ 6 ] { z }$$

Accepted Answer

A)  $\sqrt [ 9 ] { z ^ { 6 } }$ 
B)  $z ^ { 6 } \sqrt { z ^ { 4 } }$ 
C)  $z$ 
D)  $z \sqrt [ 6 ] { z ^ { 5 } }$ 
A)  $\sqrt [ 9 ] { z ^ { 6 } }$ 
B)  $z ^ { 6 } \sqrt { z ^ { 4 } }$ 
C)  $z$ 
D)  $z \sqrt [ 6 ] { z ^ { 5 } }$

Question 20

Multiply the radical expressions. $$( 4 \sqrt { 6 } + \sqrt { 2 } ) ( 2 \sqrt { 10 } - 3 \sqrt { 8 } )$$

Accepted Answer

A)  $- 16$ 
B)  $16 \sqrt { 15 } + 4 \sqrt { 5 } - 48 \sqrt { 3 } - 12$ 
C)  $32 \sqrt { 15 } + 8 \sqrt { 5 } - 192 \sqrt { 3 } - 12$ 
D)  $16 \sqrt { 15 } - 12$ 
A)  $- 16$ 
B)  $16 \sqrt { 15 } + 4 \sqrt { 5 } - 48 \sqrt { 3 } - 12$ 
C)  $32 \sqrt { 15 } + 8 \sqrt { 5 } - 192 \sqrt { 3 } - 12$ 
D)  $16 \sqrt { 15 } - 12$

Simplify the expression. $\frac { \sqrt { - 4 } } { \sqrt { 121 } }$

Rationalize the denominator. $\frac { 7 + \sqrt { 50 y } } { \sqrt { 8 } - 5 }$

Use a calculator to approximate the expression. Round to four decimal places, if necessary. $\sqrt { 6 ^ { 3 } }$

Multiply the radical expressions. $- 5 \sqrt { y } ( \sqrt { y } + 10 )$

Simplify the radical. $\sqrt [ 3 ] { 72 }$

Simplify the complex number. Write the answer in the form a + bi. $\frac { - 12 + \sqrt { - 8 } } { 2 }$

Rationalize the denominator. $\frac { 3 } { 9 - \sqrt { 5 } }$

Write the domain of the function in interval notation. $f ( x ) = \sqrt [ 3 ] { x - 12 }$

Convert the expression to radical form and simplify. $( - 64 ) ^ { 1 / 3 }$

Solve the radical equation, if possible. $\sqrt { 2 x - 8 } = \sqrt { 11 + 4 x }$

Find the length of the third side of the triangle by using the Pythagorean theorem.

Simplify the expression. $\frac { \sqrt { - 100 } } { \sqrt { - 25 } }$

Simplify the radical. $\sqrt { 30 }$

Simplify the expression by using the properties of rational exponents. Write the final answer using positive exponents only. $\left( a ^ { 1 / 5 } a ^ { 1 / 6 } \right) ^ { 30 }$

Add or subtract the radical expressions as indicated, if possible. $z ^ { 2 } \sqrt { 18 z } + 7 \sqrt { 200 z }$

Simplify the radical. $\sqrt { 140 }$

Evaluate the root without using a calculator or note that root is not a real number. $- \sqrt { 0.49 }$

Multiply the radicals with different indices. Write the answer in radical form and simplify. $\sqrt [ 3 ] { z ^ { 5 } } \cdot \sqrt [ 6 ] { z }$

Multiply the radical expressions. $( 4 \sqrt { 6 } + \sqrt { 2 } ) ( 2 \sqrt { 10 } - 3 \sqrt { 8 } )$

Linear Equations and Inequalities in One Variable

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Exam 6: Radicals and Complex Numbers

Simplify the expression. −4121\frac { \sqrt { - 4 } } { \sqrt { 121 } }121​−4​​

Rationalize the denominator. 7+50y8−5\frac { 7 + \sqrt { 50 y } } { \sqrt { 8 } - 5 }8​−57+50y​​

Use a calculator to approximate the expression. Round to four decimal places, if necessary. 63\sqrt { 6 ^ { 3 } }63​

Multiply the radical expressions. −5y(y+10)- 5 \sqrt { y } ( \sqrt { y } + 10 )−5y​(y​+10)

Simplify the radical. 723\sqrt [ 3 ] { 72 }372​

Simplify the complex number. Write the answer in the form a + bi. −12+−82\frac { - 12 + \sqrt { - 8 } } { 2 }2−12+−8​​

Rationalize the denominator. 39−5\frac { 3 } { 9 - \sqrt { 5 } }9−5​3​

Write the domain of the function in interval notation. f(x)=x−123f ( x ) = \sqrt [ 3 ] { x - 12 }f(x)=3x−12​

Convert the expression to radical form and simplify. (−64)1/3( - 64 ) ^ { 1 / 3 }(−64)1/3

Solve the radical equation, if possible. 2x−8=11+4x\sqrt { 2 x - 8 } = \sqrt { 11 + 4 x }2x−8​=11+4x​

Find the length of the third side of the triangle by using the Pythagorean theorem.

Simplify the expression. −100−25\frac { \sqrt { - 100 } } { \sqrt { - 25 } }−25​−100​​

Simplify the radical. 30\sqrt { 30 }30​

Simplify the expression by using the properties of rational exponents. Write the final answer using positive exponents only. (a1/5a1/6)30\left( a ^ { 1 / 5 } a ^ { 1 / 6 } \right) ^ { 30 }(a1/5a1/6)30

Add or subtract the radical expressions as indicated, if possible. z218z+7200zz ^ { 2 } \sqrt { 18 z } + 7 \sqrt { 200 z }z218z​+7200z​

Simplify the radical. 140\sqrt { 140 }140​

Evaluate the root without using a calculator or note that root is not a real number. −0.49- \sqrt { 0.49 }−0.49​

Multiply the radicals with different indices. Write the answer in radical form and simplify. z53⋅z6\sqrt [ 3 ] { z ^ { 5 } } \cdot \sqrt [ 6 ] { z }3z5​⋅6z​

Multiply the radical expressions. (46+2)(210−38)( 4 \sqrt { 6 } + \sqrt { 2 } ) ( 2 \sqrt { 10 } - 3 \sqrt { 8 } )(46​+2​)(210​−38​)

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables and Functions

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Simplify the expression. $\frac { \sqrt { - 4 } } { \sqrt { 121 } }$

Rationalize the denominator. $\frac { 7 + \sqrt { 50 y } } { \sqrt { 8 } - 5 }$

Use a calculator to approximate the expression. Round to four decimal places, if necessary. $\sqrt { 6 ^ { 3 } }$

Multiply the radical expressions. $- 5 \sqrt { y } ( \sqrt { y } + 10 )$

Simplify the radical. $\sqrt [ 3 ] { 72 }$

Simplify the complex number. Write the answer in the form a + bi. $\frac { - 12 + \sqrt { - 8 } } { 2 }$

Rationalize the denominator. $\frac { 3 } { 9 - \sqrt { 5 } }$

Write the domain of the function in interval notation. $f ( x ) = \sqrt [ 3 ] { x - 12 }$

Convert the expression to radical form and simplify. $( - 64 ) ^ { 1 / 3 }$

Solve the radical equation, if possible. $\sqrt { 2 x - 8 } = \sqrt { 11 + 4 x }$

Simplify the expression. $\frac { \sqrt { - 100 } } { \sqrt { - 25 } }$

Simplify the radical. $\sqrt { 30 }$

Simplify the expression by using the properties of rational exponents. Write the final answer using positive exponents only. $\left( a ^ { 1 / 5 } a ^ { 1 / 6 } \right) ^ { 30 }$

Add or subtract the radical expressions as indicated, if possible. $z ^ { 2 } \sqrt { 18 z } + 7 \sqrt { 200 z }$

Simplify the radical. $\sqrt { 140 }$

Evaluate the root without using a calculator or note that root is not a real number. $- \sqrt { 0.49 }$

Multiply the radicals with different indices. Write the answer in radical form and simplify. $\sqrt [ 3 ] { z ^ { 5 } } \cdot \sqrt [ 6 ] { z }$

Multiply the radical expressions. $( 4 \sqrt { 6 } + \sqrt { 2 } ) ( 2 \sqrt { 10 } - 3 \sqrt { 8 } )$