Question 1

Add or subtract the radical expressions as indicated, if possible. $$8 \sqrt [ 5 ] { x ^ { 6 } } - x \sqrt [ 5 ] { x }$$

Accepted Answer

A)  $8 x \sqrt [ 5 ] { x }$ 
B)  $8 x \sqrt [ 5 ] { x ^ { 6 } }$ 
C)  $7 x \sqrt [ 5 ] { x }$ 
D)  Cannot be simplified further 
A)  $8 x \sqrt [ 5 ] { x }$ 
B)  $8 x \sqrt [ 5 ] { x ^ { 6 } }$ 
C)  $7 x \sqrt [ 5 ] { x }$ 
D)  Cannot be simplified further

Question 2

Convert the expression to radical notation. $$\left( 18 y ^ { 2 } \right) ^ { 1 / 7 }$$

Accepted Answer

The answer of Convert the expression to radical notation. \[\left(...

Question 3

Multiply the radical expressions and simplify your answer. $$( \sqrt { 108 } - 1 ) ( \sqrt { 3 } + 5 )$$

Accepted Answer

A)  13 
B)  $13 + 29 \sqrt { 3 }$ 
C)  $319 + 5 \sqrt { 108 } - \sqrt { 3 }$ 
D)  $\sqrt { 321 } - 5$ 
A)  13 
B)  $13 + 29 \sqrt { 3 }$ 
C)  $319 + 5 \sqrt { 108 } - \sqrt { 3 }$ 
D)  $\sqrt { 321 } - 5$

Question 4

Write the expression by using rational exponents rather than radical notation. $7 \sqrt [ 7 ] { x ^ { 3 } }$

Accepted Answer

A)  $( 7 x ) ^ { 3 / 7 }$ 
B)  $7 x ^ { 7 / 3 }$ 
C)  $\frac { 7 } { x ^ { 3 / 7 } }$ 
D)  $7 x ^ { 3 / 7 }$ 
A)  $( 7 x ) ^ { 3 / 7 }$ 
B)  $7 x ^ { 7 / 3 }$ 
C)  $\frac { 7 } { x ^ { 3 / 7 } }$ 
D)  $7 x ^ { 3 / 7 }$

Question 5

Simplify using the division property of radicals. $\frac { \sqrt { 27 z } } { \sqrt { 3 z } }$

Accepted Answer

A)  $\sqrt { 3 z }$ 
B)  $3 z$ 
C)  3 
D)  9 
A)  $\sqrt { 3 z }$ 
B)  $3 z$ 
C)  3 
D)  9

Question 6

Find the length of the third side of the triangle. Write your answer as a simplified radical.

Accepted Answer

A)  $6 \sqrt { 16 }$ 
B)  $2 \sqrt { 34 }$ 
C)  $3 \sqrt { 24 }$ 
D)  $4 \sqrt { 34 }$ 
A)  $6 \sqrt { 16 }$ 
B)  $2 \sqrt { 34 }$ 
C)  $3 \sqrt { 24 }$ 
D)  $4 \sqrt { 34 }$

Question 7

Simplify the expression, if possible. $$\left( \frac { 1 } { 27 } \right) ^ { - 2 / 3 } - \left( \frac { 1 } { 9 } \right) ^ { - 1 / 2 }$$

Accepted Answer

A)  6 
B)  $- \frac { 2 } { 9 }$ 
C)  $\frac { 1 } { 6 }$ 
D)  Not a real number 
A)  6 
B)  $- \frac { 2 } { 9 }$ 
C)  $\frac { 1 } { 6 }$ 
D)  Not a real number

Question 8

Solve the equation. $$\sqrt { y } = 3$$

Accepted Answer

The answer of Solve the equation. \[\sqrt { y }...

Question 9

Simplify the radical. Assume that all variables represent positive real numbers. $\sqrt { \frac { p ^ { 11 } } { p ^ { 5 } } }$

Accepted Answer

A)  $p ^ { 3 }$ 
B)  $( \sqrt { p } ) ^ { 3 }$ 
C)  $p ^ { 8 }$ 
D)  $( \sqrt { p } ) ^ { 8 }$ 
A)  $p ^ { 3 }$ 
B)  $( \sqrt { p } ) ^ { 3 }$ 
C)  $p ^ { 8 }$ 
D)  $( \sqrt { p } ) ^ { 8 }$

Question 10

Evaluate the root without using a calculator or note that root is not a real number. $\sqrt [ 3 ] { 27 }$

Accepted Answer

A)  4 
B)  3 
C)  $- 3$ 
D)  Not a real number 
A)  4 
B)  3 
C)  $- 3$ 
D)  Not a real number

Question 11

Divide the complex numbers. Write the answer in the form a + bi. $$\frac { 5 } { 1 + 3 i }$$

Accepted Answer

A)  $\frac { 5 } { 8 } + \frac { 15 } { 8 } i$ 
B)  $\frac { 1 } { 2 } + \frac { 3 } { 2 } i$ 
C)  $\frac { 1 } { 2 } - \frac { 3 } { 2 } i$ 
D)  $\frac { 5 } { 8 } - \frac { 15 } { 8 } i$ 
A)  $\frac { 5 } { 8 } + \frac { 15 } { 8 } i$ 
B)  $\frac { 1 } { 2 } + \frac { 3 } { 2 } i$ 
C)  $\frac { 1 } { 2 } - \frac { 3 } { 2 } i$ 
D)  $\frac { 5 } { 8 } - \frac { 15 } { 8 } i$

Question 12

Divide the complex numbers. Write the answer in the form a + bi. $$\frac { - 8 + 3 i } { 5 + 7 i }$$

Accepted Answer

The answer of Divide the complex numbers. Write the answer...

Question 13

Simplify the expression. Assume all variables represent positive real numbers. $$( \sqrt { 3 } ) ^ { 2 }$$

Accepted Answer

A)  6 
B)  3 
C)  1.5 
D)  9 
A)  6 
B)  3 
C)  1.5 
D)  9

Question 14

Write the expression using rational exponents. Then simplify and convert back to radical notation. $\sqrt [ 3 ] { 27 x ^ { 3 } y ^ { 2 } z }$

Accepted Answer

A)  $3 \sqrt [ 3 ] { y ^ { 2 } z }$ 
B)  $3 \sqrt [ 3 ] { x y ^ { 2 } z }$ 
C)  $3 x \sqrt [ 3 ] { y ^ { 2 } z }$ 
D)  $x \sqrt [ 3 ] { 27 y ^ { 2 } z }$ 
A)  $3 \sqrt [ 3 ] { y ^ { 2 } z }$ 
B)  $3 \sqrt [ 3 ] { x y ^ { 2 } z }$ 
C)  $3 x \sqrt [ 3 ] { y ^ { 2 } z }$ 
D)  $x \sqrt [ 3 ] { 27 y ^ { 2 } z }$

Question 15

Multiply. Write the answer in the form a + bi. $$\left( \frac { 5 } { 2 } + 2 i \right) \left( \frac { 1 } { 4 } - 6 i \right)$$

Accepted Answer

The answer of Multiply. Write the answer in the form...

Question 16

Evaluate the root without using a calculator or note that root is not a real number. $\sqrt [ 3 ] { - 125 }$

Accepted Answer

A)  $- 5$ 
B)  6 
C)  5 
D)  Not a real number 
A)  $- 5$ 
B)  6 
C)  5 
D)  Not a real number

Question 17

Simplify the expression, if possible. $512 ^ { 2 / 3 }$

Accepted Answer

A)  -64 
B)  $\frac { 1024 } { 3 }$ 
C)  64 
D)  Not a real number 
A)  -64 
B)  $\frac { 1024 } { 3 }$ 
C)  64 
D)  Not a real number

Question 18

Rationalize the denominator. $\frac { - 18 } { \sqrt [ 3 ] { 10 } }$

Accepted Answer

A)  $\frac { 5 \sqrt [ 3 ] { 100 } } { - 9 }$ 
B)  $\frac { - 9 \sqrt [ 3 ] { 100 } } { 5 }$ 
C)  $\frac { - 9 \sqrt [ 3 ] { 10 } } { 5 }$ 
D)  Already rationalized 
A)  $\frac { 5 \sqrt [ 3 ] { 100 } } { - 9 }$ 
B)  $\frac { - 9 \sqrt [ 3 ] { 100 } } { 5 }$ 
C)  $\frac { - 9 \sqrt [ 3 ] { 10 } } { 5 }$ 
D)  Already rationalized

Question 19

Simplify the expression. $\sqrt { - 21 }$

Accepted Answer

A)  $21 i$ 
B)  $i \sqrt { 21 }$ 
C)  $- 21 i$ 
D)  $- i \sqrt { 21 }$ 
A)  $21 i$ 
B)  $i \sqrt { 21 }$ 
C)  $- 21 i$ 
D)  $- i \sqrt { 21 }$

Question 20

Add or subtract the radical expressions as indicated, if possible. $\sqrt { 12 x } - 5 \sqrt { 3 y } + \sqrt { 48 x }$

Accepted Answer

A)  $2 \sqrt { 15 x } - 5 \sqrt { 3 y }$ 
B)  $6 \sqrt { 3 x } - 5 \sqrt { 3 y }$ 
C)  $\sqrt { 60 x + 15 y }$ 
D)  $\sqrt { 3 x y }$ 
A)  $2 \sqrt { 15 x } - 5 \sqrt { 3 y }$ 
B)  $6 \sqrt { 3 x } - 5 \sqrt { 3 y }$ 
C)  $\sqrt { 60 x + 15 y }$ 
D)  $\sqrt { 3 x y }$

Add or subtract the radical expressions as indicated, if possible. $8 \sqrt [ 5 ] { x ^ { 6 } } - x \sqrt [ 5 ] { x }$

Convert the expression to radical notation. $\left( 18 y ^ { 2 } \right) ^ { 1 / 7 }$

Multiply the radical expressions and simplify your answer. $( \sqrt { 108 } - 1 ) ( \sqrt { 3 } + 5 )$

Write the expression by using rational exponents rather than radical notation. $7 \sqrt [ 7 ] { x ^ { 3 } }$

Simplify using the division property of radicals. $\frac { \sqrt { 27 z } } { \sqrt { 3 z } }$

Find the length of the third side of the triangle. Write your answer as a simplified radical.

Simplify the expression, if possible. $\left( \frac { 1 } { 27 } \right) ^ { - 2 / 3 } - \left( \frac { 1 } { 9 } \right) ^ { - 1 / 2 }$

Solve the equation. $\sqrt { y } = 3$

Simplify the radical. Assume that all variables represent positive real numbers. $\sqrt { \frac { p ^ { 11 } } { p ^ { 5 } } }$

Evaluate the root without using a calculator or note that root is not a real number. $\sqrt [ 3 ] { 27 }$

Divide the complex numbers. Write the answer in the form a + bi. $\frac { 5 } { 1 + 3 i }$

Divide the complex numbers. Write the answer in the form a + bi. $\frac { - 8 + 3 i } { 5 + 7 i }$

Simplify the expression. Assume all variables represent positive real numbers. $( \sqrt { 3 } ) ^ { 2 }$

Write the expression using rational exponents. Then simplify and convert back to radical notation. $\sqrt [ 3 ] { 27 x ^ { 3 } y ^ { 2 } z }$

Multiply. Write the answer in the form a + bi. $\left( \frac { 5 } { 2 } + 2 i \right) \left( \frac { 1 } { 4 } - 6 i \right)$

Evaluate the root without using a calculator or note that root is not a real number. $\sqrt [ 3 ] { - 125 }$

Simplify the expression, if possible. $512 ^ { 2 / 3 }$

Rationalize the denominator. $\frac { - 18 } { \sqrt [ 3 ] { 10 } }$

Simplify the expression. $\sqrt { - 21 }$

Add or subtract the radical expressions as indicated, if possible. $\sqrt { 12 x } - 5 \sqrt { 3 y } + \sqrt { 48 x }$

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

Add or subtract the radical expressions as indicated, if possible. 8x65−xx58 \sqrt [ 5 ] { x ^ { 6 } } - x \sqrt [ 5 ] { x }85x6​−x5x​

Convert the expression to radical notation. (18y2)1/7\left( 18 y ^ { 2 } \right) ^ { 1 / 7 }(18y2)1/7

Multiply the radical expressions and simplify your answer. (108−1)(3+5)( \sqrt { 108 } - 1 ) ( \sqrt { 3 } + 5 )(108​−1)(3​+5)

Write the expression by using rational exponents rather than radical notation. 7x377 \sqrt [ 7 ] { x ^ { 3 } }77x3​

Simplify using the division property of radicals. 27z3z\frac { \sqrt { 27 z } } { \sqrt { 3 z } }3z​27z​​

Find the length of the third side of the triangle. Write your answer as a simplified radical.

Simplify the expression, if possible. (127)−2/3−(19)−1/2\left( \frac { 1 } { 27 } \right) ^ { - 2 / 3 } - \left( \frac { 1 } { 9 } \right) ^ { - 1 / 2 }(271​)−2/3−(91​)−1/2

Solve the equation. y=3\sqrt { y } = 3y​=3

Simplify the radical. Assume that all variables represent positive real numbers. p11p5\sqrt { \frac { p ^ { 11 } } { p ^ { 5 } } }p5p11​​

Evaluate the root without using a calculator or note that root is not a real number. 273\sqrt [ 3 ] { 27 }327​

Divide the complex numbers. Write the answer in the form a + bi. 51+3i\frac { 5 } { 1 + 3 i }1+3i5​

Divide the complex numbers. Write the answer in the form a + bi. −8+3i5+7i\frac { - 8 + 3 i } { 5 + 7 i }5+7i−8+3i​

Simplify the expression. Assume all variables represent positive real numbers. (3)2( \sqrt { 3 } ) ^ { 2 }(3​)2

Write the expression using rational exponents. Then simplify and convert back to radical notation. 27x3y2z3\sqrt [ 3 ] { 27 x ^ { 3 } y ^ { 2 } z }327x3y2z​

Multiply. Write the answer in the form a + bi. (52+2i)(14−6i)\left( \frac { 5 } { 2 } + 2 i \right) \left( \frac { 1 } { 4 } - 6 i \right)(25​+2i)(41​−6i)

Evaluate the root without using a calculator or note that root is not a real number. −1253\sqrt [ 3 ] { - 125 }3−125​

Simplify the expression, if possible. 5122/3512 ^ { 2 / 3 }5122/3

Rationalize the denominator. −18103\frac { - 18 } { \sqrt [ 3 ] { 10 } }310​−18​

Simplify the expression. −21\sqrt { - 21 }−21​

Add or subtract the radical expressions as indicated, if possible. 12x−53y+48x\sqrt { 12 x } - 5 \sqrt { 3 y } + \sqrt { 48 x }12x​−53y​+48x​

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

Add or subtract the radical expressions as indicated, if possible. $8 \sqrt [ 5 ] { x ^ { 6 } } - x \sqrt [ 5 ] { x }$

Convert the expression to radical notation. $\left( 18 y ^ { 2 } \right) ^ { 1 / 7 }$

Multiply the radical expressions and simplify your answer. $( \sqrt { 108 } - 1 ) ( \sqrt { 3 } + 5 )$

Write the expression by using rational exponents rather than radical notation. $7 \sqrt [ 7 ] { x ^ { 3 } }$

Simplify using the division property of radicals. $\frac { \sqrt { 27 z } } { \sqrt { 3 z } }$

Simplify the expression, if possible. $\left( \frac { 1 } { 27 } \right) ^ { - 2 / 3 } - \left( \frac { 1 } { 9 } \right) ^ { - 1 / 2 }$

Solve the equation. $\sqrt { y } = 3$

Simplify the radical. Assume that all variables represent positive real numbers. $\sqrt { \frac { p ^ { 11 } } { p ^ { 5 } } }$

Evaluate the root without using a calculator or note that root is not a real number. $\sqrt [ 3 ] { 27 }$

Divide the complex numbers. Write the answer in the form a + bi. $\frac { 5 } { 1 + 3 i }$

Divide the complex numbers. Write the answer in the form a + bi. $\frac { - 8 + 3 i } { 5 + 7 i }$

Simplify the expression. Assume all variables represent positive real numbers. $( \sqrt { 3 } ) ^ { 2 }$

Write the expression using rational exponents. Then simplify and convert back to radical notation. $\sqrt [ 3 ] { 27 x ^ { 3 } y ^ { 2 } z }$

Multiply. Write the answer in the form a + bi. $\left( \frac { 5 } { 2 } + 2 i \right) \left( \frac { 1 } { 4 } - 6 i \right)$

Evaluate the root without using a calculator or note that root is not a real number. $\sqrt [ 3 ] { - 125 }$

Simplify the expression, if possible. $512 ^ { 2 / 3 }$

Rationalize the denominator. $\frac { - 18 } { \sqrt [ 3 ] { 10 } }$

Simplify the expression. $\sqrt { - 21 }$

Add or subtract the radical expressions as indicated, if possible. $\sqrt { 12 x } - 5 \sqrt { 3 y } + \sqrt { 48 x }$