Question 1

Simplify the expression. Assume that all variables represent positive real numbers. $\sqrt { 64 x ^ { 2 } y ^ { 4 } z ^ { 2 } }$

Accepted Answer

A)  $64 x y ^ { 2 } z$ 
B)  $8 x ^ { 2 } x ^ { 4 } z ^ { 2 }$ 
C)  $8 x y ^ { 2 } z$ 
D)  $32 x y ^ { 2 } z$ 
A)  $64 x y ^ { 2 } z$ 
B)  $8 x ^ { 2 } x ^ { 4 } z ^ { 2 }$ 
C)  $8 x y ^ { 2 } z$ 
D)  $32 x y ^ { 2 } z$

Question 2

Multiply the radical expressions and simplify your answer. $\sqrt { 5 x ^ { 3 } } \cdot \sqrt { 18 x ^ { 6 } }$

Accepted Answer

A)  $3 \sqrt { 10 x ^ { 9 } }$ 
B)  $\sqrt { 30 x ^ { 9 } }$ 
C)  $3 x ^ { 4 } \sqrt { 10 x }$ 
D)  $9 x ^ { 4 } \sqrt { 10 x }$ 
A)  $3 \sqrt { 10 x ^ { 9 } }$ 
B)  $\sqrt { 30 x ^ { 9 } }$ 
C)  $3 x ^ { 4 } \sqrt { 10 x }$ 
D)  $9 x ^ { 4 } \sqrt { 10 x }$

Question 3

Multiply the radicals with different indices. Write the answer in radical form and simplify. $\sqrt [ 4 ] { 9 } \cdot \sqrt { 3 }$

Accepted Answer

A)  3 
B)  $\sqrt [ 4 ] { 27 }$ 
C)  $\sqrt [ 8 ] { 27 }$ 
D)  Cannot be simplified further 
A)  3 
B)  $\sqrt [ 4 ] { 27 }$ 
C)  $\sqrt [ 8 ] { 27 }$ 
D)  Cannot be simplified further

Question 4

Divide the complex numbers. Write the answer in the form a + bi. $$\frac { 3 - i } { 2 + i }$$

Accepted Answer

A)  $- \frac { 3 } { 2 }$ 
B)  $1 - i$ 
C)  $\frac { 5 } { 4 } - \frac { 5 } { 4 } i$ 
D)  $\frac { 3 } { 2 } - i$ 
A)  $- \frac { 3 } { 2 }$ 
B)  $1 - i$ 
C)  $\frac { 5 } { 4 } - \frac { 5 } { 4 } i$ 
D)  $\frac { 3 } { 2 } - i$

Question 5

Multiply the radicals with different indices. Write the answer in radical form and simplify. $\sqrt [ 4 ] { 7 } \cdot \sqrt { 7 }$

Accepted Answer

A)  $\sqrt [ 8 ] { 7 }$ 
B)  $\sqrt [ 4 ] { 49 }$ 
C)  7 
D)  $\sqrt [ 4 ] { 343 }$ 
A)  $\sqrt [ 8 ] { 7 }$ 
B)  $\sqrt [ 4 ] { 49 }$ 
C)  7 
D)  $\sqrt [ 4 ] { 343 }$

Question 6

Simplify the expression by using the properties of rational exponents. Write the final answer using positive exponents only. $$\left( \frac { 2 z ^ { - 2 / 3 } } { t ^ { 5 / 3 } } \right) ^ { - 3 }$$

Accepted Answer

The answer of Simplify the expression by using the properties...

Question 7

Add the radical expressions, if possible. $5 \sqrt { 10 } + 6 \sqrt { 10 }$

Accepted Answer

A)  $30 \sqrt { 10 }$ 
B)  $11 \sqrt { 20 }$ 
C)  $11 \sqrt { 10 }$ 
D)  Cannot be simplified further 
A)  $30 \sqrt { 10 }$ 
B)  $11 \sqrt { 20 }$ 
C)  $11 \sqrt { 10 }$ 
D)  Cannot be simplified further

Question 8

Simplify the expression. $\sqrt { - 16 }$

Accepted Answer

A)  $i \sqrt { 4 }$ 
B)  $- 4 i$ 
C)  $16 i$ 
D)  $4 i$ 
A)  $i \sqrt { 4 }$ 
B)  $- 4 i$ 
C)  $16 i$ 
D)  $4 i$

Question 9

Multiply the radical expressions. $\sqrt { 3 } \cdot \sqrt { 24 }$

Accepted Answer

A)  $6 \sqrt { 2 }$ 
B)  $3 \sqrt { 3 }$ 
C)  $36 \sqrt { 2 }$ 
D)  $2 \sqrt { 6 }$ 
A)  $6 \sqrt { 2 }$ 
B)  $3 \sqrt { 3 }$ 
C)  $36 \sqrt { 2 }$ 
D)  $2 \sqrt { 6 }$

Question 10

What is the conjugate of $$- 14 + 5 \sqrt { x }$$

Accepted Answer

The answer of What is the conjugate of \[- 14...

Question 11

Rationalize the denominator. $\frac { 2 - 4 \sqrt { 2 } } { \sqrt { 2 } + 1 }$

Accepted Answer

A)  $2 - 5 \sqrt { 2 }$ 
B)  $\frac { 2 \sqrt { 2 } - 8 } { 3 }$ 
C)  $\frac { 6 \sqrt { 2 } - 10 } { 3 }$ 
D)  $6 \sqrt { 2 } - 10$ 
A)  $2 - 5 \sqrt { 2 }$ 
B)  $\frac { 2 \sqrt { 2 } - 8 } { 3 }$ 
C)  $\frac { 6 \sqrt { 2 } - 10 } { 3 }$ 
D)  $6 \sqrt { 2 } - 10$

Question 12

Multiply the radical expressions. $2 \sqrt { 5 } \cdot 2 \sqrt { 15 }$

Accepted Answer

A)  $20 \sqrt { 3 }$ 
B)  $4 \sqrt { 3 }$ 
C)  $8 \sqrt { 5 }$ 
D)  $100 \sqrt { 2 }$ 
A)  $20 \sqrt { 3 }$ 
B)  $4 \sqrt { 3 }$ 
C)  $8 \sqrt { 5 }$ 
D)  $100 \sqrt { 2 }$

Question 13

Simplify the expression. Assume that all variables represent positive real numbers. $$\sqrt { \frac { a ^ { 10 } } { b ^ { 2 } } }$$

Accepted Answer

A)  $\frac { a ^ { 8 } } { b }$ 
B)  $\frac { a ^ { 5 } } { b ^ { 2 } }$ 
C)  $\frac { a ^ { 5 } } { b }$ 
D)  $\frac { a ^ { 8 } } { b ^ { 2 } }$ 
A)  $\frac { a ^ { 8 } } { b }$ 
B)  $\frac { a ^ { 5 } } { b ^ { 2 } }$ 
C)  $\frac { a ^ { 5 } } { b }$ 
D)  $\frac { a ^ { 8 } } { b ^ { 2 } }$

Question 14

Simplify the radical. Assume that all variables represent positive real numbers. $$\sqrt { \frac { 162 z ^ { 17 } } { 3 z ^ { 4 } } }$$

Accepted Answer

A)  $9 z ^ { 6 } \sqrt { 6 z }$ 
B)  $3 z ^ { 6 } \sqrt { 6 z }$ 
C)  $3 z \sqrt { 6 z ^ { 11 } }$ 
D)  $3 \sqrt { 6 z ^ { 13 } }$ 
A)  $9 z ^ { 6 } \sqrt { 6 z }$ 
B)  $3 z ^ { 6 } \sqrt { 6 z }$ 
C)  $3 z \sqrt { 6 z ^ { 11 } }$ 
D)  $3 \sqrt { 6 z ^ { 13 } }$

Question 15

Solve the equation. $$\sqrt { z + 8 } = 3$$

Accepted Answer

The answer of Solve the equation. \[\sqrt { z +...

Question 16

Add or subtract the radical expressions as indicated, if possible. $$- 2 \sqrt [ 3 ] { 128 } + \sqrt [ 3 ] { 2 } - \sqrt [ 3 ] { 81 }$$

Accepted Answer

A)  $- 3 \sqrt [ 3 ] { 101 } + \sqrt [ 3 ] { 2 }$ 
B)  $- 10 \sqrt [ 3 ] { 5 }$ 
C)  $- 7 \sqrt [ 3 ] { 2 } - 3 \sqrt [ 3 ] { 3 }$ 
D)  Cannot be simplified further 
A)  $- 3 \sqrt [ 3 ] { 101 } + \sqrt [ 3 ] { 2 }$ 
B)  $- 10 \sqrt [ 3 ] { 5 }$ 
C)  $- 7 \sqrt [ 3 ] { 2 } - 3 \sqrt [ 3 ] { 3 }$ 
D)  Cannot be simplified further

Question 17

Simplify the expression by using the properties of rational exponents. Write the final answer using positive exponents only. $$\left( x ^ { 4 } y ^ { 8 } \right) ^ { 2 / 3 }$$

Accepted Answer

A)  $x ^ { 4 } y ^ { 16 / 3 }$ 
B)  $x ^ { 8 / 3 } y ^ { 16 / 3 }$ 
C)  $x ^ { 14 / 3 } y ^ { 26 / 3 }$ 
D)  $\frac { 2 } { 3 } x ^ { 4 } y ^ { 8 }$ 
A)  $x ^ { 4 } y ^ { 16 / 3 }$ 
B)  $x ^ { 8 / 3 } y ^ { 16 / 3 }$ 
C)  $x ^ { 14 / 3 } y ^ { 26 / 3 }$ 
D)  $\frac { 2 } { 3 } x ^ { 4 } y ^ { 8 }$

Question 18

Solve the radical equation, if possible. $$\sqrt { 3 a - 7 } = 2 - \sqrt { 3 a + 1 }$$

Accepted Answer

A)  $\left\{ \frac { 10 } { 3 } \right\}$ 
B)  $\left\{ \frac { 32 } { 3 } \right\}$ 
C)  $\left\{ \frac { 8 } { 3 } \right\}$ 
D)  \{ \} 
A)  $\left\{ \frac { 10 } { 3 } \right\}$ 
B)  $\left\{ \frac { 32 } { 3 } \right\}$ 
C)  $\left\{ \frac { 8 } { 3 } \right\}$ 
D)  \{ \}

Question 19

Solve the radical equation, if possible. $$5 t = \sqrt { 25 t ^ { 2 } + 4 t - 17 }$$

Accepted Answer

A)  $\left\{ \frac { 17 } { 4 } \right\}$ 
B)  $\{ 5 \}$ 
C)  $\left\{ \frac { 4 } { 17 } \right\}$ 
D)  \{ \} 
A)  $\left\{ \frac { 17 } { 4 } \right\}$ 
B)  $\{ 5 \}$ 
C)  $\left\{ \frac { 4 } { 17 } \right\}$ 
D)  \{ \}

Question 20

Multiply the radical expressions. $$\sqrt { 2 } ( \sqrt { 32 } - \sqrt { 3 } )$$

Accepted Answer

A)  $2 \sqrt { 32 } - 6$ 
B)  $8 + \sqrt { 6 }$ 
C)  $8 - \sqrt { 6 }$ 
D)  $8 - \sqrt { 3 }$ 
A)  $2 \sqrt { 32 } - 6$ 
B)  $8 + \sqrt { 6 }$ 
C)  $8 - \sqrt { 6 }$ 
D)  $8 - \sqrt { 3 }$

Simplify the expression. Assume that all variables represent positive real numbers. $\sqrt { 64 x ^ { 2 } y ^ { 4 } z ^ { 2 } }$

Multiply the radical expressions and simplify your answer. $\sqrt { 5 x ^ { 3 } } \cdot \sqrt { 18 x ^ { 6 } }$

Multiply the radicals with different indices. Write the answer in radical form and simplify. $\sqrt [ 4 ] { 9 } \cdot \sqrt { 3 }$

Divide the complex numbers. Write the answer in the form a + bi. $\frac { 3 - i } { 2 + i }$

Multiply the radicals with different indices. Write the answer in radical form and simplify. $\sqrt [ 4 ] { 7 } \cdot \sqrt { 7 }$

Simplify the expression by using the properties of rational exponents. Write the final answer using positive exponents only. $\left( \frac { 2 z ^ { - 2 / 3 } } { t ^ { 5 / 3 } } \right) ^ { - 3 }$

Add the radical expressions, if possible. $5 \sqrt { 10 } + 6 \sqrt { 10 }$

Simplify the expression. $\sqrt { - 16 }$

Multiply the radical expressions. $\sqrt { 3 } \cdot \sqrt { 24 }$

What is the conjugate of $- 14 + 5 \sqrt { x }$

Rationalize the denominator. $\frac { 2 - 4 \sqrt { 2 } } { \sqrt { 2 } + 1 }$

Multiply the radical expressions. $2 \sqrt { 5 } \cdot 2 \sqrt { 15 }$

Simplify the expression. Assume that all variables represent positive real numbers. $\sqrt { \frac { a ^ { 10 } } { b ^ { 2 } } }$

Simplify the radical. Assume that all variables represent positive real numbers. $\sqrt { \frac { 162 z ^ { 17 } } { 3 z ^ { 4 } } }$

Solve the equation. $\sqrt { z + 8 } = 3$

Add or subtract the radical expressions as indicated, if possible. $- 2 \sqrt [ 3 ] { 128 } + \sqrt [ 3 ] { 2 } - \sqrt [ 3 ] { 81 }$

Simplify the expression by using the properties of rational exponents. Write the final answer using positive exponents only. $\left( x ^ { 4 } y ^ { 8 } \right) ^ { 2 / 3 }$

Solve the radical equation, if possible. $\sqrt { 3 a - 7 } = 2 - \sqrt { 3 a + 1 }$

Solve the radical equation, if possible. $5 t = \sqrt { 25 t ^ { 2 } + 4 t - 17 }$

Multiply the radical expressions. $\sqrt { 2 } ( \sqrt { 32 } - \sqrt { 3 } )$

Linear Equations and Inequalities in One Variable

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Exam 6: Radicals and Complex Numbers

Simplify the expression. Assume that all variables represent positive real numbers. 64x2y4z2\sqrt { 64 x ^ { 2 } y ^ { 4 } z ^ { 2 } }64x2y4z2​

Multiply the radical expressions and simplify your answer. 5x3⋅18x6\sqrt { 5 x ^ { 3 } } \cdot \sqrt { 18 x ^ { 6 } }5x3​⋅18x6​

Multiply the radicals with different indices. Write the answer in radical form and simplify. 94⋅3\sqrt [ 4 ] { 9 } \cdot \sqrt { 3 }49​⋅3​

Divide the complex numbers. Write the answer in the form a + bi. 3−i2+i\frac { 3 - i } { 2 + i }2+i3−i​

Multiply the radicals with different indices. Write the answer in radical form and simplify. 74⋅7\sqrt [ 4 ] { 7 } \cdot \sqrt { 7 }47​⋅7​

Simplify the expression by using the properties of rational exponents. Write the final answer using positive exponents only. (2z−2/3t5/3)−3\left( \frac { 2 z ^ { - 2 / 3 } } { t ^ { 5 / 3 } } \right) ^ { - 3 }(t5/32z−2/3​)−3

Add the radical expressions, if possible. 510+6105 \sqrt { 10 } + 6 \sqrt { 10 }510​+610​

Simplify the expression. −16\sqrt { - 16 }−16​

Multiply the radical expressions. 3⋅24\sqrt { 3 } \cdot \sqrt { 24 }3​⋅24​

What is the conjugate of −14+5x- 14 + 5 \sqrt { x }−14+5x​

Rationalize the denominator. 2−422+1\frac { 2 - 4 \sqrt { 2 } } { \sqrt { 2 } + 1 }2​+12−42​​

Multiply the radical expressions. 25⋅2152 \sqrt { 5 } \cdot 2 \sqrt { 15 }25​⋅215​

Simplify the expression. Assume that all variables represent positive real numbers. a10b2\sqrt { \frac { a ^ { 10 } } { b ^ { 2 } } }b2a10​​

Simplify the radical. Assume that all variables represent positive real numbers. 162z173z4\sqrt { \frac { 162 z ^ { 17 } } { 3 z ^ { 4 } } }3z4162z17​​

Solve the equation. z+8=3\sqrt { z + 8 } = 3z+8​=3

Add or subtract the radical expressions as indicated, if possible. −21283+23−813- 2 \sqrt [ 3 ] { 128 } + \sqrt [ 3 ] { 2 } - \sqrt [ 3 ] { 81 }−23128​+32​−381​

Simplify the expression by using the properties of rational exponents. Write the final answer using positive exponents only. (x4y8)2/3\left( x ^ { 4 } y ^ { 8 } \right) ^ { 2 / 3 }(x4y8)2/3

Solve the radical equation, if possible. 3a−7=2−3a+1\sqrt { 3 a - 7 } = 2 - \sqrt { 3 a + 1 }3a−7​=2−3a+1​

Solve the radical equation, if possible. 5t=25t2+4t−175 t = \sqrt { 25 t ^ { 2 } + 4 t - 17 }5t=25t2+4t−17​

Multiply the radical expressions. 2(32−3)\sqrt { 2 } ( \sqrt { 32 } - \sqrt { 3 } )2​(32​−3​)

Linear Equations and Inequalities in One Variable

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Online: Transformations, Piecewise-Defined Functions, and Probability

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Simplify the expression. Assume that all variables represent positive real numbers. $\sqrt { 64 x ^ { 2 } y ^ { 4 } z ^ { 2 } }$

Multiply the radical expressions and simplify your answer. $\sqrt { 5 x ^ { 3 } } \cdot \sqrt { 18 x ^ { 6 } }$

Multiply the radicals with different indices. Write the answer in radical form and simplify. $\sqrt [ 4 ] { 9 } \cdot \sqrt { 3 }$

Divide the complex numbers. Write the answer in the form a + bi. $\frac { 3 - i } { 2 + i }$

Multiply the radicals with different indices. Write the answer in radical form and simplify. $\sqrt [ 4 ] { 7 } \cdot \sqrt { 7 }$

Simplify the expression by using the properties of rational exponents. Write the final answer using positive exponents only. $\left( \frac { 2 z ^ { - 2 / 3 } } { t ^ { 5 / 3 } } \right) ^ { - 3 }$

Add the radical expressions, if possible. $5 \sqrt { 10 } + 6 \sqrt { 10 }$

Simplify the expression. $\sqrt { - 16 }$

Multiply the radical expressions. $\sqrt { 3 } \cdot \sqrt { 24 }$

What is the conjugate of $- 14 + 5 \sqrt { x }$

Rationalize the denominator. $\frac { 2 - 4 \sqrt { 2 } } { \sqrt { 2 } + 1 }$

Multiply the radical expressions. $2 \sqrt { 5 } \cdot 2 \sqrt { 15 }$

Simplify the expression. Assume that all variables represent positive real numbers. $\sqrt { \frac { a ^ { 10 } } { b ^ { 2 } } }$

Simplify the radical. Assume that all variables represent positive real numbers. $\sqrt { \frac { 162 z ^ { 17 } } { 3 z ^ { 4 } } }$

Solve the equation. $\sqrt { z + 8 } = 3$

Add or subtract the radical expressions as indicated, if possible. $- 2 \sqrt [ 3 ] { 128 } + \sqrt [ 3 ] { 2 } - \sqrt [ 3 ] { 81 }$

Simplify the expression by using the properties of rational exponents. Write the final answer using positive exponents only. $\left( x ^ { 4 } y ^ { 8 } \right) ^ { 2 / 3 }$

Solve the radical equation, if possible. $\sqrt { 3 a - 7 } = 2 - \sqrt { 3 a + 1 }$

Solve the radical equation, if possible. $5 t = \sqrt { 25 t ^ { 2 } + 4 t - 17 }$

Multiply the radical expressions. $\sqrt { 2 } ( \sqrt { 32 } - \sqrt { 3 } )$