Question 1

Simplify the radical expression. Assume a is unrestricted. $\sqrt [ 3 ] { 8 a ^ { 3 } }$

Accepted Answer

A)  $2 a ^ { 3 }$ 
B)  8a 
C)  $8 a ^ { 3 }$ 
D)  2a 
E)  not real 
A)  $2 a ^ { 3 }$ 
B)  8a 
C)  $8 a ^ { 3 }$ 
D)  2a 
E)  not real

Question 2

Find f (6) for $f ( x ) = \sqrt { x - 8 }$ .

Accepted Answer

A)  2 
B)  -2 
C)  3 
D)  not a real number 
A)  2 
B)  -2 
C)  3 
D)  not a real number

Question 3

Simplify by combining like radicals. The variable represents a positive real number. $\sqrt { 175 m } - \sqrt { 18 m } + \sqrt { 128 m }$

Accepted Answer

The answer of Simplify by combining like radicals. The variable...

Question 4

Simplify the radical expression. The variable represents a positive real number. $\sqrt { 28 x ^ { 2 } }$

Accepted Answer

The answer of Simplify the radical expression. The variable represents...

Question 5

Divide. Write the answer in the form $a + b i$ . $\frac { 3 + 2 i } { 3 + i }$

Accepted Answer

A)  $\frac { 5 } { 2 } + \frac { 3 } { 10 } i$ 
B)  $6 - \frac { 3 } { 10 } i$ 
C)  $\frac { 3 } { 2 } - \frac { 5 } { 2 } i$ 
D)  $\frac { 11 } { 10 } + 6 i$ 
E)  $\frac { 11 } { 10 } + \frac { 3 } { 10 } i$ 
A)  $\frac { 5 } { 2 } + \frac { 3 } { 10 } i$ 
B)  $6 - \frac { 3 } { 10 } i$ 
C)  $\frac { 3 } { 2 } - \frac { 5 } { 2 } i$ 
D)  $\frac { 11 } { 10 } + 6 i$ 
E)  $\frac { 11 } { 10 } + \frac { 3 } { 10 } i$

Question 6

Evaluate the radical expression, if possible, without using a calculator. $\sqrt [ 4 ] { - 625 }$

Accepted Answer

A)  5 
B)  -5 
C)  -625 
D)  625 
E)  not real 
A)  5 
B)  -5 
C)  -625 
D)  625 
E)  not real

Question 7

Tell why the following expression is not in simplified radical form. Then simplify the expression. $\frac { \sqrt { 27 } } { 5 }$

Accepted Answer

There is a perfect s

Question 8

Rationalize the denominator. $\frac { 1 } { \sqrt [ 3 ] { 6 } }$

Accepted Answer

The answer of Rationalize the denominator. \(\frac { 1 }...

Question 9

Simplify: $\sqrt { 54 }$

Accepted Answer

A)  $3 \sqrt { 6 }$ 
B)  $6 \sqrt { 3 }$ 
C)  $8 \sqrt { 6 }$ 
D)  $6 \sqrt { 8 }$ 
A)  $3 \sqrt { 6 }$ 
B)  $6 \sqrt { 3 }$ 
C)  $8 \sqrt { 6 }$ 
D)  $6 \sqrt { 8 }$

Question 10

Evaluate the square root, if possible, without using a calculator. $- \sqrt { 169 }$

Accepted Answer

A)  12 
B)  -12 
C)  15 
D)  -13 
E)  not real 
A)  12 
B)  -12 
C)  15 
D)  -13 
E)  not real

Question 11

Perform the indicated operation. Simplify, if possible. $\sqrt [ 3 ] { 6 x ^ { 5 } y ^ { 6 } } \cdot \sqrt [ 3 ] { 6 x ^ { 5 } y ^ { 6 } }$

Accepted Answer

A)  $x ^ { 3 } y ^ { 4 } \cdot \sqrt [ 3 ] { 36 x }$ 
B)  $6 x ^ { 5 } y ^ { 6 }$ 
C)  $6 x ^ { 3 } y ^ { 4 } \cdot \sqrt [ 3 ] { 36 x }$ 
D)  $\sqrt [ 3 ] { 36 x ^ { 10 } y ^ { 12 } }$ 
A)  $x ^ { 3 } y ^ { 4 } \cdot \sqrt [ 3 ] { 36 x }$ 
B)  $6 x ^ { 5 } y ^ { 6 }$ 
C)  $6 x ^ { 3 } y ^ { 4 } \cdot \sqrt [ 3 ] { 36 x }$ 
D)  $\sqrt [ 3 ] { 36 x ^ { 10 } y ^ { 12 } }$

Question 12

Perform the indicated operation. Leave answer in $a + b i$ form. $( 4 + 2 i ) ( 1 - 9 i )$

Accepted Answer

A)  $- 18 i ^ { 2 } - 34 i + 4$ 
B)  $- 14 - 34 i$ 
C)  $22 - 34 i$ 
D)  $22$ 
A)  $- 18 i ^ { 2 } - 34 i + 4$ 
B)  $- 14 - 34 i$ 
C)  $22 - 34 i$ 
D)  $22$

Question 13

Multiply. Write the answer in the form $a + b i$ . $( 5 - i ) ( 2 + i )$

Accepted Answer

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

Question 14

Evaluate the expression. $( - 125 ) ^ { \frac { 1 } { 3 } }$

Accepted Answer

A)  -15 
B)  -10 
C)  -5 
D)  -16 
E)  not real 
A)  -15 
B)  -10 
C)  -5 
D)  -16 
E)  not real

Question 15

Perform the operation. Write the answer in a+bi form. $( 2 + 5 i ) + ( 10 - 11 i )$

Accepted Answer

A)  $11 + 2 i$ 
B)  $13 - 6 i$ 
C)  $14 - 2 i$ 
D)  $12 - 6 i$ 
E)  $10 + 9 i$ 
A)  $11 + 2 i$ 
B)  $13 - 6 i$ 
C)  $14 - 2 i$ 
D)  $12 - 6 i$ 
E)  $10 + 9 i$

Question 16

Rationalize the denominator. $\frac { \sqrt { 29 } - \sqrt { 2 } } { \sqrt { 2 } + \sqrt { 29 } }$

Accepted Answer

The answer of Rationalize the denominator. \(\frac { \sqrt {...

Question 17

Simplify the expression. $36 ^ { - \frac { 1 } { 2 } }$

Accepted Answer

The answer of Simplify the expression. \(36 ^ { -...

Question 18

Multiply and simplify, if possible. $( 3 \sqrt { 7 } + 2 ) ( \sqrt { 7 } - 2 )$

Accepted Answer

The answer of Multiply and simplify, if possible. \(( 3...

Question 19

In a $30 ^ { \circ } - 60 ^ { \circ } - 90 ^ { \circ }$ triangle, the length of the shorter leg is $5 \sqrt { 5 }$ cm. Find the length of the hypotenuse. Give the exact answer.

Accepted Answer

The answer of In a \(30 ^ { \circ }...

Question 20

Simplify the radical expression. $\sqrt { 160 }$

Accepted Answer

A)  $4 + \sqrt { 10 }$ 
B)  40 
C)  $4 \sqrt { 10 }$ 
D)  $10 + \sqrt { 4 }$ 
E)  $10 \sqrt { 4 }$ 
A)  $4 + \sqrt { 10 }$ 
B)  40 
C)  $4 \sqrt { 10 }$ 
D)  $10 + \sqrt { 4 }$ 
E)  $10 \sqrt { 4 }$

Simplify the radical expression. Assume a is unrestricted. $\sqrt [ 3 ] { 8 a ^ { 3 } }$

Find f (6) for $f ( x ) = \sqrt { x - 8 }$ .

Simplify by combining like radicals. The variable represents a positive real number. $\sqrt { 175 m } - \sqrt { 18 m } + \sqrt { 128 m }$

Simplify the radical expression. The variable represents a positive real number. $\sqrt { 28 x ^ { 2 } }$

Divide. Write the answer in the form $a + b i$ . $\frac { 3 + 2 i } { 3 + i }$

Evaluate the radical expression, if possible, without using a calculator. $\sqrt [ 4 ] { - 625 }$

Tell why the following expression is not in simplified radical form. Then simplify the expression. $\frac { \sqrt { 27 } } { 5 }$

Rationalize the denominator. $\frac { 1 } { \sqrt [ 3 ] { 6 } }$

Simplify: $\sqrt { 54 }$

Evaluate the square root, if possible, without using a calculator. $- \sqrt { 169 }$

Perform the indicated operation. Simplify, if possible. $\sqrt [ 3 ] { 6 x ^ { 5 } y ^ { 6 } } \cdot \sqrt [ 3 ] { 6 x ^ { 5 } y ^ { 6 } }$

Perform the indicated operation. Leave answer in $a + b i$ form. $( 4 + 2 i ) ( 1 - 9 i )$

Multiply. Write the answer in the form $a + b i$ . $( 5 - i ) ( 2 + i )$

Evaluate the expression. $( - 125 ) ^ { \frac { 1 } { 3 } }$

Perform the operation. Write the answer in a+bi form. $( 2 + 5 i ) + ( 10 - 11 i )$

Rationalize the denominator. $\frac { \sqrt { 29 } - \sqrt { 2 } } { \sqrt { 2 } + \sqrt { 29 } }$

Simplify the expression. $36 ^ { - \frac { 1 } { 2 } }$

Multiply and simplify, if possible. $( 3 \sqrt { 7 } + 2 ) ( \sqrt { 7 } - 2 )$

In a $30 ^ { \circ } - 60 ^ { \circ } - 90 ^ { \circ }$ triangle, the length of the shorter leg is $5 \sqrt { 5 }$ cm. Find the length of the hypotenuse. Give the exact answer.

Simplify the radical expression. $\sqrt { 160 }$

A Review of Basic Algebra

Graphs, Equations of Lines, and Functions

Systems of Equations

Inequalities

Exponents, Polynomials, and Polynomial Functions

Rational Expression and Equations

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Conic Sections; More Graphing

Miscellaneous Topics

Filters

Exam 7: Radical Expressions and Equations

Simplify the radical expression. Assume a is unrestricted. 8a33\sqrt [ 3 ] { 8 a ^ { 3 } }38a3​

Find f (6) for f(x)=x−8f ( x ) = \sqrt { x - 8 }f(x)=x−8​ .

Simplify by combining like radicals. The variable represents a positive real number. 175m−18m+128m\sqrt { 175 m } - \sqrt { 18 m } + \sqrt { 128 m }175m​−18m​+128m​

Simplify the radical expression. The variable represents a positive real number. 28x2\sqrt { 28 x ^ { 2 } }28x2​

Divide. Write the answer in the form a+bia + b ia+bi . 3+2i3+i\frac { 3 + 2 i } { 3 + i }3+i3+2i​

Evaluate the radical expression, if possible, without using a calculator. −6254\sqrt [ 4 ] { - 625 }4−625​

Tell why the following expression is not in simplified radical form. Then simplify the expression. 275\frac { \sqrt { 27 } } { 5 }527​​

Rationalize the denominator. 163\frac { 1 } { \sqrt [ 3 ] { 6 } }36​1​

Simplify: 54\sqrt { 54 }54​

Evaluate the square root, if possible, without using a calculator. −169- \sqrt { 169 }−169​

Perform the indicated operation. Simplify, if possible. 6x5y63⋅6x5y63\sqrt [ 3 ] { 6 x ^ { 5 } y ^ { 6 } } \cdot \sqrt [ 3 ] { 6 x ^ { 5 } y ^ { 6 } }36x5y6​⋅36x5y6​

Perform the indicated operation. Leave answer in a+bia + b ia+bi form. (4+2i)(1−9i)( 4 + 2 i ) ( 1 - 9 i )(4+2i)(1−9i)

Multiply. Write the answer in the form a+bia + b ia+bi . (5−i)(2+i)( 5 - i ) ( 2 + i )(5−i)(2+i)

Evaluate the expression. (−125)13( - 125 ) ^ { \frac { 1 } { 3 } }(−125)31​

Perform the operation. Write the answer in a+bi form. (2+5i)+(10−11i)( 2 + 5 i ) + ( 10 - 11 i )(2+5i)+(10−11i)

Rationalize the denominator. 29−22+29\frac { \sqrt { 29 } - \sqrt { 2 } } { \sqrt { 2 } + \sqrt { 29 } }2​+29​29​−2​​

Simplify the expression. 36−1236 ^ { - \frac { 1 } { 2 } }36−21​

Multiply and simplify, if possible. (37+2)(7−2)( 3 \sqrt { 7 } + 2 ) ( \sqrt { 7 } - 2 )(37​+2)(7​−2)

In a 30∘−60∘−90∘30 ^ { \circ } - 60 ^ { \circ } - 90 ^ { \circ }30∘−60∘−90∘ triangle, the length of the shorter leg is 555 \sqrt { 5 }55​ cm. Find the length of the hypotenuse. Give the exact answer.

Simplify the radical expression. 160\sqrt { 160 }160​

A Review of Basic Algebra

Graphs, Equations of Lines, and Functions

Systems of Equations

Inequalities

Exponents, Polynomials, and Polynomial Functions

Rational Expression and Equations

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Conic Sections; More Graphing

Miscellaneous Topics

Filters

Simplify the radical expression. Assume a is unrestricted. $\sqrt [ 3 ] { 8 a ^ { 3 } }$

Find f (6) for $f ( x ) = \sqrt { x - 8 }$ .

Simplify by combining like radicals. The variable represents a positive real number. $\sqrt { 175 m } - \sqrt { 18 m } + \sqrt { 128 m }$

Simplify the radical expression. The variable represents a positive real number. $\sqrt { 28 x ^ { 2 } }$

Divide. Write the answer in the form $a + b i$ . $\frac { 3 + 2 i } { 3 + i }$

Evaluate the radical expression, if possible, without using a calculator. $\sqrt [ 4 ] { - 625 }$

Tell why the following expression is not in simplified radical form. Then simplify the expression. $\frac { \sqrt { 27 } } { 5 }$

Rationalize the denominator. $\frac { 1 } { \sqrt [ 3 ] { 6 } }$

Simplify: $\sqrt { 54 }$

Evaluate the square root, if possible, without using a calculator. $- \sqrt { 169 }$

Perform the indicated operation. Simplify, if possible. $\sqrt [ 3 ] { 6 x ^ { 5 } y ^ { 6 } } \cdot \sqrt [ 3 ] { 6 x ^ { 5 } y ^ { 6 } }$

Perform the indicated operation. Leave answer in $a + b i$ form. $( 4 + 2 i ) ( 1 - 9 i )$

Multiply. Write the answer in the form $a + b i$ . $( 5 - i ) ( 2 + i )$

Evaluate the expression. $( - 125 ) ^ { \frac { 1 } { 3 } }$

Perform the operation. Write the answer in a+bi form. $( 2 + 5 i ) + ( 10 - 11 i )$

Rationalize the denominator. $\frac { \sqrt { 29 } - \sqrt { 2 } } { \sqrt { 2 } + \sqrt { 29 } }$

Simplify the expression. $36 ^ { - \frac { 1 } { 2 } }$

Multiply and simplify, if possible. $( 3 \sqrt { 7 } + 2 ) ( \sqrt { 7 } - 2 )$

In a $30 ^ { \circ } - 60 ^ { \circ } - 90 ^ { \circ }$ triangle, the length of the shorter leg is $5 \sqrt { 5 }$ cm. Find the length of the hypotenuse. Give the exact answer.

Simplify the radical expression. $\sqrt { 160 }$