Question 1

Multiply the radical expressions. $( \sqrt { 11 } + k ) ^ { 2 }$

Accepted Answer

A)  $11 + 2 k \sqrt { 11 } + k ^ { 2 }$ 
B)  $121 + 2 k \sqrt { 11 } + k ^ { 2 }$ 
C)  $121 + k ^ { 2 }$ 
D)  $11 + k ^ { 2 }$ 
A)  $11 + 2 k \sqrt { 11 } + k ^ { 2 }$ 
B)  $121 + 2 k \sqrt { 11 } + k ^ { 2 }$ 
C)  $121 + k ^ { 2 }$ 
D)  $11 + k ^ { 2 }$

Question 2

Subtract the radical expressions. Assume that all variables represent positive real numbers. $3 \sqrt { 72 y ^ { 3 } } - \sqrt { 2 y }$

Accepted Answer

A)  $17 \sqrt { 2 y ^ { 3 } - 2 y }$ 
B)  $3 \sqrt { 72 y ^ { 3 } - 2 y }$ 
C)  $( 18 y - 1 ) \sqrt { 2 y }$ 
D)  Cannot be simplified further 
A)  $17 \sqrt { 2 y ^ { 3 } - 2 y }$ 
B)  $3 \sqrt { 72 y ^ { 3 } - 2 y }$ 
C)  $( 18 y - 1 ) \sqrt { 2 y }$ 
D)  Cannot be simplified further

Question 3

Multiply the radical expressions. $$\left( \frac { 1 } { 3 } \sqrt { x } - \frac { 3 } { 2 } \sqrt { y } \right) ^ { 2 }$$

Accepted Answer

A)  $\frac { 1 } { 9 } x - \sqrt { x y } + \frac { 9 } { 4 } y$ 
B)  $\frac { 1 } { 9 } x + \frac { 9 } { 4 } y$ 
C)  $\frac { 1 } { 9 } x - \frac { 9 } { 4 } y$ 
D)  $\frac { 1 } { 9 } x + \frac { 6 } { 5 } \sqrt { x y } - \frac { 9 } { 4 } y$ 
A)  $\frac { 1 } { 9 } x - \sqrt { x y } + \frac { 9 } { 4 } y$ 
B)  $\frac { 1 } { 9 } x + \frac { 9 } { 4 } y$ 
C)  $\frac { 1 } { 9 } x - \frac { 9 } { 4 } y$ 
D)  $\frac { 1 } { 9 } x + \frac { 6 } { 5 } \sqrt { x y } - \frac { 9 } { 4 } y$

Question 4

Simplify the expression by using the properties of rational exponents. Write the final answer using positive exponents only. $$\left( \frac { 81 s ^ { 12 } r ^ { - 4 } } { 16 s ^ { - 4 } r ^ { 4 } } \right) ^ { 3 / 4 }$$

Accepted Answer

A)  $\frac { 3 s ^ { 12 } } { 2 r ^ { 6 } }$ 
B)  $\frac { 27 s ^ { 6 } } { 8 }$ 
C)  $\frac { 3 s ^ { 16 } r ^ { 8 } } { 2 }$ 
D)  $\frac { 27 s ^ { 12 } } { 8 r ^ { 6 } }$ 
A)  $\frac { 3 s ^ { 12 } } { 2 r ^ { 6 } }$ 
B)  $\frac { 27 s ^ { 6 } } { 8 }$ 
C)  $\frac { 3 s ^ { 16 } r ^ { 8 } } { 2 }$ 
D)  $\frac { 27 s ^ { 12 } } { 8 r ^ { 6 } }$

Question 5

Solve the equation. $$\sqrt { 8 t + 7 } = - 2$$

Accepted Answer

A)  $\{ - 9 \}$ 
B)  $\left\{ - \frac { 11 } { 8 } \right\}$ 
C)  $\left\{ \frac { - 3 } { 8 } \right\}$ 
D)  \{ \} 
A)  $\{ - 9 \}$ 
B)  $\left\{ - \frac { 11 } { 8 } \right\}$ 
C)  $\left\{ \frac { - 3 } { 8 } \right\}$ 
D)  \{ \}

Question 6

Multiply the radical expressions. $$( \sqrt [ 3 ] { n } - 3 ) ( \sqrt [ 3 ] { n } + 5 )$$

Accepted Answer

A)  $n + 2 \sqrt [ 3 ] { n } - 15$ 
B)  $n - 15$ 
C)  $\sqrt [ 3 ] { n ^ { 2 } } - 15$ 
D)  $\sqrt [ 3 ] { n ^ { 2 } } + 2 \sqrt [ 3 ] { n } - 15$ 
A)  $n + 2 \sqrt [ 3 ] { n } - 15$ 
B)  $n - 15$ 
C)  $\sqrt [ 3 ] { n ^ { 2 } } - 15$ 
D)  $\sqrt [ 3 ] { n ^ { 2 } } + 2 \sqrt [ 3 ] { n } - 15$

Question 7

Add or subtract the radical expressions as indicated, if possible. $$\sqrt [ 4 ] { m n } + m \sqrt [ 4 ] { n }$$

Accepted Answer

A)  $( m + 1 ) \sqrt [ 4 ] { m n + n }$ 
B)  $\sqrt [ 4 ] { m n + m ^ { 4 } \mathrm { n } }$ 
C)  $( m + 1 ) \sqrt [ 4 ] { m n + m ^ { 4 } \mathrm { n } }$ 
D)  Cannot be simplified further 
A)  $( m + 1 ) \sqrt [ 4 ] { m n + n }$ 
B)  $\sqrt [ 4 ] { m n + m ^ { 4 } \mathrm { n } }$ 
C)  $( m + 1 ) \sqrt [ 4 ] { m n + m ^ { 4 } \mathrm { n } }$ 
D)  Cannot be simplified further

Question 8

Solve the radical equation, if possible. $$\sqrt { 49 m ^ { 2 } - 4 m + 10 } = 7 m - 8$$

Accepted Answer

A)  $\left\{ \frac { 1 } { 2 } \right\}$ 
B)  $\{ - 2,2 \}$ 
C)  $\left\{ - \frac { 1 } { 2 } , \frac { 1 } { 2 } \right\}$ 
D)  \{ \} 
A)  $\left\{ \frac { 1 } { 2 } \right\}$ 
B)  $\{ - 2,2 \}$ 
C)  $\left\{ - \frac { 1 } { 2 } , \frac { 1 } { 2 } \right\}$ 
D)  \{ \}

Question 9

Evaluate the root without using a calculator or note that root is not a real number. $\sqrt [ 8 ] { 256 }$

Accepted Answer

A)  4 
B)  2 
C)  16 
D)  Not a real number 
A)  4 
B)  2 
C)  16 
D)  Not a real number

Question 10

Write the expression by using rational exponents rather than radical notation. $\frac { 16 } { \sqrt [ 5 ] { x } }$

Accepted Answer

A)  $16 x ^ { 1 / 5 }$ 
B)  $16 x ^ { - 5 }$ 
C)  $16 x ^ { - 1 / 5 }$ 
D)  $( 16 x ) ^ { - 1 / 5 }$ 
A)  $16 x ^ { 1 / 5 }$ 
B)  $16 x ^ { - 5 }$ 
C)  $16 x ^ { - 1 / 5 }$ 
D)  $( 16 x ) ^ { - 1 / 5 }$

Question 11

Evaluate the function for k (-9), k (-8), k (-7), k (-6), and k (-3). Then write the domain of the function in interval notation. $k ( x ) = \sqrt { x + 7 }$

Accepted Answer

k (-9): Not a real n

Question 12

Evaluate the root without using a calculator or note that root is not a real number. $\sqrt [ 4 ] { - 625 }$

Accepted Answer

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

Question 13

Multiply. Write the answer in the form a + bi. $$( - 3 - 4 i ) \cdot ( 7 + 10 i )$$

Accepted Answer

A)  19 
B)  $- 21 - 40 i$ 
C)  $- 61 - 58 i$ 
D)  $19 - 58 i$ 
A)  19 
B)  $- 21 - 40 i$ 
C)  $- 61 - 58 i$ 
D)  $19 - 58 i$

Question 14

Simplify the expression. Assume that all variables represent positive real numbers. $- \sqrt [ 4 ] { \frac { 16 y ^ { 16 } } { 81 } }$

Accepted Answer

A)  $\frac { 2 y ^ { 4 } } { 3 }$ 
B)  $- \frac { 2 y ^ { 4 } } { 3 }$ 
C)  $\frac { 3 } { 2 y ^ { 4 } }$ 
D)  $- \frac { 3 } { 2 y ^ { 4 } }$ 
A)  $\frac { 2 y ^ { 4 } } { 3 }$ 
B)  $- \frac { 2 y ^ { 4 } } { 3 }$ 
C)  $\frac { 3 } { 2 y ^ { 4 } }$ 
D)  $- \frac { 3 } { 2 y ^ { 4 } }$

Question 15

Simplify the expression. Assume that all variables represent positive real numbers. $$\sqrt [ 3 ] { 64 a ^ { 12 } b ^ { 6 } }$$

Accepted Answer

A)  $61 a ^ { 9 } b ^ { 3 }$ 
B)  $2 a ^ { 3 } b ^ { 3 }$ 
C)  $- 4 a ^ { 4 } b ^ { 2 }$ 
D)  $4 a ^ { 4 } b ^ { 2 }$ 
A)  $61 a ^ { 9 } b ^ { 3 }$ 
B)  $2 a ^ { 3 } b ^ { 3 }$ 
C)  $- 4 a ^ { 4 } b ^ { 2 }$ 
D)  $4 a ^ { 4 } b ^ { 2 }$

Question 16

Evaluate the root without using a calculator or note that root is not a real number. $\sqrt { 0.16 }$

Accepted Answer

A)  $0.0256$ 
B)  $- 0.4$ 
C)  $0.4$ 
D)  Not a real number 
A)  $0.0256$ 
B)  $- 0.4$ 
C)  $0.4$ 
D)  Not a real number

Question 17

Multiply the radical expressions. $$( 6 - \sqrt { 13 } ) ( 6 + \sqrt { 13 } )$$

Accepted Answer

A)  $- 133$ 
B)  23 
C)  49 
D)  $36 - \sqrt { 13 }$ 
A)  $- 133$ 
B)  23 
C)  49 
D)  $36 - \sqrt { 13 }$

Question 18

Simplify. $$i ^ { 31 }$$

Accepted Answer

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

Question 19

Solve the equation. $$5 + \sqrt { 9 - 9 x } = 2$$

Accepted Answer

The answer of Solve the equation. \[5 + \sqrt {...

Question 20

What is the definition of the number i?

Accepted Answer

A)  $i = - \sqrt { 1 }$ 
B)  $i = \sqrt { - 1 }$ 
C)  $i = - 1$ 
D)  $i = ( - 1 ) ^ { 2 }$ 
A)  $i = - \sqrt { 1 }$ 
B)  $i = \sqrt { - 1 }$ 
C)  $i = - 1$ 
D)  $i = ( - 1 ) ^ { 2 }$

Multiply the radical expressions. $( \sqrt { 11 } + k ) ^ { 2 }$

Subtract the radical expressions. Assume that all variables represent positive real numbers. $3 \sqrt { 72 y ^ { 3 } } - \sqrt { 2 y }$

Multiply the radical expressions. $\left( \frac { 1 } { 3 } \sqrt { x } - \frac { 3 } { 2 } \sqrt { y } \right) ^ { 2 }$

Simplify the expression by using the properties of rational exponents. Write the final answer using positive exponents only. $\left( \frac { 81 s ^ { 12 } r ^ { - 4 } } { 16 s ^ { - 4 } r ^ { 4 } } \right) ^ { 3 / 4 }$

Solve the equation. $\sqrt { 8 t + 7 } = - 2$

Multiply the radical expressions. $( \sqrt [ 3 ] { n } - 3 ) ( \sqrt [ 3 ] { n } + 5 )$

Add or subtract the radical expressions as indicated, if possible. $\sqrt [ 4 ] { m n } + m \sqrt [ 4 ] { n }$

Solve the radical equation, if possible. $\sqrt { 49 m ^ { 2 } - 4 m + 10 } = 7 m - 8$

Evaluate the root without using a calculator or note that root is not a real number. $\sqrt [ 8 ] { 256 }$

Write the expression by using rational exponents rather than radical notation. $\frac { 16 } { \sqrt [ 5 ] { x } }$

Evaluate the function for k (-9), k (-8), k (-7), k (-6), and k (-3). Then write the domain of the function in interval notation. $k ( x ) = \sqrt { x + 7 }$

Evaluate the root without using a calculator or note that root is not a real number. $\sqrt [ 4 ] { - 625 }$

Multiply. Write the answer in the form a + bi. $( - 3 - 4 i ) \cdot ( 7 + 10 i )$

Simplify the expression. Assume that all variables represent positive real numbers. $- \sqrt [ 4 ] { \frac { 16 y ^ { 16 } } { 81 } }$

Simplify the expression. Assume that all variables represent positive real numbers. $\sqrt [ 3 ] { 64 a ^ { 12 } b ^ { 6 } }$

Evaluate the root without using a calculator or note that root is not a real number. $\sqrt { 0.16 }$

Multiply the radical expressions. $( 6 - \sqrt { 13 } ) ( 6 + \sqrt { 13 } )$

Simplify. $i ^ { 31 }$

Solve the equation. $5 + \sqrt { 9 - 9 x } = 2$

What is the definition of the number i?

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

Multiply the radical expressions. (11+k)2( \sqrt { 11 } + k ) ^ { 2 }(11​+k)2

Subtract the radical expressions. Assume that all variables represent positive real numbers. 372y3−2y3 \sqrt { 72 y ^ { 3 } } - \sqrt { 2 y }372y3​−2y​

Multiply the radical expressions. (13x−32y)2\left( \frac { 1 } { 3 } \sqrt { x } - \frac { 3 } { 2 } \sqrt { y } \right) ^ { 2 }(31​x​−23​y​)2

Simplify the expression by using the properties of rational exponents. Write the final answer using positive exponents only. (81s12r−416s−4r4)3/4\left( \frac { 81 s ^ { 12 } r ^ { - 4 } } { 16 s ^ { - 4 } r ^ { 4 } } \right) ^ { 3 / 4 }(16s−4r481s12r−4​)3/4

Solve the equation. 8t+7=−2\sqrt { 8 t + 7 } = - 28t+7​=−2

Multiply the radical expressions. (n3−3)(n3+5)( \sqrt [ 3 ] { n } - 3 ) ( \sqrt [ 3 ] { n } + 5 )(3n​−3)(3n​+5)

Add or subtract the radical expressions as indicated, if possible. mn4+mn4\sqrt [ 4 ] { m n } + m \sqrt [ 4 ] { n }4mn​+m4n​

Solve the radical equation, if possible. 49m2−4m+10=7m−8\sqrt { 49 m ^ { 2 } - 4 m + 10 } = 7 m - 849m2−4m+10​=7m−8

Evaluate the root without using a calculator or note that root is not a real number. 2568\sqrt [ 8 ] { 256 }8256​

Write the expression by using rational exponents rather than radical notation. 16x5\frac { 16 } { \sqrt [ 5 ] { x } }5x​16​

Evaluate the function for k (-9), k (-8), k (-7), k (-6), and k (-3). Then write the domain of the function in interval notation. k(x)=x+7k ( x ) = \sqrt { x + 7 }k(x)=x+7​

Evaluate the root without using a calculator or note that root is not a real number. −6254\sqrt [ 4 ] { - 625 }4−625​

Multiply. Write the answer in the form a + bi. (−3−4i)⋅(7+10i)( - 3 - 4 i ) \cdot ( 7 + 10 i )(−3−4i)⋅(7+10i)

Simplify the expression. Assume that all variables represent positive real numbers. −16y16814- \sqrt [ 4 ] { \frac { 16 y ^ { 16 } } { 81 } }−48116y16​​

Simplify the expression. Assume that all variables represent positive real numbers. 64a12b63\sqrt [ 3 ] { 64 a ^ { 12 } b ^ { 6 } }364a12b6​

Evaluate the root without using a calculator or note that root is not a real number. 0.16\sqrt { 0.16 }0.16​

Multiply the radical expressions. (6−13)(6+13)( 6 - \sqrt { 13 } ) ( 6 + \sqrt { 13 } )(6−13​)(6+13​)

Simplify. i31i ^ { 31 }i31

Solve the equation. 5+9−9x=25 + \sqrt { 9 - 9 x } = 25+9−9x​=2

What is the definition of the number i?

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

Multiply the radical expressions. $( \sqrt { 11 } + k ) ^ { 2 }$

Subtract the radical expressions. Assume that all variables represent positive real numbers. $3 \sqrt { 72 y ^ { 3 } } - \sqrt { 2 y }$

Multiply the radical expressions. $\left( \frac { 1 } { 3 } \sqrt { x } - \frac { 3 } { 2 } \sqrt { y } \right) ^ { 2 }$

Simplify the expression by using the properties of rational exponents. Write the final answer using positive exponents only. $\left( \frac { 81 s ^ { 12 } r ^ { - 4 } } { 16 s ^ { - 4 } r ^ { 4 } } \right) ^ { 3 / 4 }$

Solve the equation. $\sqrt { 8 t + 7 } = - 2$

Multiply the radical expressions. $( \sqrt [ 3 ] { n } - 3 ) ( \sqrt [ 3 ] { n } + 5 )$

Add or subtract the radical expressions as indicated, if possible. $\sqrt [ 4 ] { m n } + m \sqrt [ 4 ] { n }$

Solve the radical equation, if possible. $\sqrt { 49 m ^ { 2 } - 4 m + 10 } = 7 m - 8$

Evaluate the root without using a calculator or note that root is not a real number. $\sqrt [ 8 ] { 256 }$

Write the expression by using rational exponents rather than radical notation. $\frac { 16 } { \sqrt [ 5 ] { x } }$

Evaluate the function for k (-9), k (-8), k (-7), k (-6), and k (-3). Then write the domain of the function in interval notation. $k ( x ) = \sqrt { x + 7 }$

Evaluate the root without using a calculator or note that root is not a real number. $\sqrt [ 4 ] { - 625 }$

Multiply. Write the answer in the form a + bi. $( - 3 - 4 i ) \cdot ( 7 + 10 i )$

Simplify the expression. Assume that all variables represent positive real numbers. $- \sqrt [ 4 ] { \frac { 16 y ^ { 16 } } { 81 } }$

Simplify the expression. Assume that all variables represent positive real numbers. $\sqrt [ 3 ] { 64 a ^ { 12 } b ^ { 6 } }$

Evaluate the root without using a calculator or note that root is not a real number. $\sqrt { 0.16 }$

Multiply the radical expressions. $( 6 - \sqrt { 13 } ) ( 6 + \sqrt { 13 } )$

Simplify. $i ^ { 31 }$

Solve the equation. $5 + \sqrt { 9 - 9 x } = 2$