Question 1

Simplify: $\sqrt { - 4 } \cdot \sqrt { - 100 }$

Accepted Answer

A)  $20 i$ 
B)  $20$ 
C)  $- 20i$ 
D)  $- 20$ 
A)  $20 i$ 
B)  $20$ 
C)  $- 20i$ 
D)  $- 20$

Question 2

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

Accepted Answer

A)  $11 - 3 i$ 
B)  $10 - 4 i$ 
C)  $8 - 4 i$ 
D)  $9 + 6 i$ 
E)  $12 - 3 i$ 
A)  $11 - 3 i$ 
B)  $10 - 4 i$ 
C)  $8 - 4 i$ 
D)  $9 + 6 i$ 
E)  $12 - 3 i$

Question 3

Evaluate the expression. $16 ^ { \frac { 1 } { 4 } }$

Accepted Answer

The answer of Evaluate the expression. \(16 ^ { \frac...

Question 4

Simplify the radical expression. All variables represent positive real numbers. $\sqrt [ 3 ] { 625 x ^ { 6 } y ^ { 3 } }$

Accepted Answer

The answer of Simplify the radical expression. All variables represent...

Question 5

Simplify by combining like radicals. The variable represents a positive real number. $\sqrt { 216 m } - \sqrt { 192 m } + \sqrt { 588 m }$

Accepted Answer

A)  $6 \sqrt { 6 m } + 6 \sqrt { 3 m }$ 
B)  $14 \sqrt { 6 m } + 6 \sqrt { 3 m }$ 
C)  $6 \sqrt { 6 m } + 14 \sqrt { 3 m }$ 
D)  $14 \sqrt { 6 m } - 6 \sqrt { 3 m }$ 
E)  $6 \sqrt { 6 m } - 6 \sqrt { 3 m }$ 
A)  $6 \sqrt { 6 m } + 6 \sqrt { 3 m }$ 
B)  $14 \sqrt { 6 m } + 6 \sqrt { 3 m }$ 
C)  $6 \sqrt { 6 m } + 14 \sqrt { 3 m }$ 
D)  $14 \sqrt { 6 m } - 6 \sqrt { 3 m }$ 
E)  $6 \sqrt { 6 m } - 6 \sqrt { 3 m }$

Question 6

Simplify the radical expression. All variables represent positive real numbers. $\sqrt [ 4 ] { 243 x ^ { 12 } y ^ { 4 } }$

Accepted Answer

A)  $3 x y ^ { 4 } \sqrt { 3 x y }$ 
B)  $3 x ^ { 4 } y \sqrt [ 4 ] { 3 }$ 
C)  $3 x ^ { 3 } y ^ { 2 } \sqrt [ 4 ] { 3 }$ 
D)  $3 x ^ { 3 } y \sqrt [ 4 ] { 3 }$ 
E)  $3 x ^ { 3 } y + \sqrt [ 4 ] { 3 }$ 
A)  $3 x y ^ { 4 } \sqrt { 3 x y }$ 
B)  $3 x ^ { 4 } y \sqrt [ 4 ] { 3 }$ 
C)  $3 x ^ { 3 } y ^ { 2 } \sqrt [ 4 ] { 3 }$ 
D)  $3 x ^ { 3 } y \sqrt [ 4 ] { 3 }$ 
E)  $3 x ^ { 3 } y + \sqrt [ 4 ] { 3 }$

Question 7

Simplify $\sqrt { x ^ { 2 } - 14 x + 49 }$ . Assume all variables are unrestricted and use absolute value symbols when necessary.

Accepted Answer

A)  x-7 
B)  $( x - 7 ) ^ { 2 }$ 
C)  7|x| 
D)  | x-7| 
A)  x-7 
B)  $( x - 7 ) ^ { 2 }$ 
C)  7|x| 
D)  | x-7|

Question 8

In the expression $\sqrt [ 3 ] { 8 x ^ { 6 } }$ , the __________ is 3 and $8 x ^ { 6 }$ is the __________.

Accepted Answer

The answer of In the expression \(\sqrt [ 3 ]...

Question 9

Simplify by combining like radicals. $\sqrt { 98 } - \sqrt { 72 } - \sqrt { 128 }$

Accepted Answer

The answer of Simplify by combining like radicals. \(\sqrt {...

Question 10

Solve: $6 \sqrt { x + 2 } = x - 5$

Accepted Answer

The answer of Solve: \(6 \sqrt { x + 2...

Question 11

Simplify the cube root. $\sqrt [ 3 ] { - 8 a ^ { 3 } }$

Accepted Answer

The answer of Simplify the cube root. \(\sqrt [ 3...

Question 12

Radical expressions such as $\sqrt [ 3 ] { 3 }$   and $5 \sqrt [ 3 ] { 3 }$ with the same index and the same radicand are called __________ radicals.

Accepted Answer

A)  simplified 
B)  like 
C)  cubed 
D)  perfect 
E)  squared 
A)  simplified 
B)  like 
C)  cubed 
D)  perfect 
E)  squared

Question 13

Simplify by combining like radicals. The variable represents a positive real number. $\sqrt [ 3 ] { 54 x } + \sqrt [ 3 ] { 2 x }$

Accepted Answer

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

Question 14

Multiply and simplify, if possible. $( 5 \sqrt { 3 } + 2 ) ( \sqrt { 3 } - 2 )$

Accepted Answer

A)  $11 + 8 \sqrt { 3 }$ 
B)  $- 11 + 8 \sqrt { 3 }$ 
C)  $8 + 11 \sqrt { 3 }$ 
D)  $11 - 8 \sqrt { 3 }$ 
E)  $- 11 - 8 \sqrt { 3 }$ 
A)  $11 + 8 \sqrt { 3 }$ 
B)  $- 11 + 8 \sqrt { 3 }$ 
C)  $8 + 11 \sqrt { 3 }$ 
D)  $11 - 8 \sqrt { 3 }$ 
E)  $- 11 - 8 \sqrt { 3 }$

Question 15

Find the domain and range of the function $f ( x )$ . $f ( x ) = \sqrt { x } + 1$

Accepted Answer

A)  $D = [ 0 , \infty ) ; R = [ - 2 , \infty )$ 
B)  $D = [ - \infty , - 2 ) ; R = ( - \infty , \infty )$ 
C)  $D = [ 0 , \infty ) ; R = ( 1 , \infty )$ 
D)  $D = [ - \infty , - 2 ) ; R = ( - 2 , \infty )$ 
E)  $D = [ 0 , \infty ) ; R = [ 1 , \infty )$ 
A)  $D = [ 0 , \infty ) ; R = [ - 2 , \infty )$ 
B)  $D = [ - \infty , - 2 ) ; R = ( - \infty , \infty )$ 
C)  $D = [ 0 , \infty ) ; R = ( 1 , \infty )$ 
D)  $D = [ - \infty , - 2 ) ; R = ( - 2 , \infty )$ 
E)  $D = [ 0 , \infty ) ; R = [ 1 , \infty )$

Question 16

Simplify by combining like radicals. $\sqrt [ 3 ] { 4 } - \sqrt [ 3 ] { 32 }$

Accepted Answer

A)  $\sqrt [ 3 ] { 3 } - \sqrt [ 3 ] { 2 }$ 
B)  $- 2 \sqrt [ 3 ] { 4 }$ 
C)  $2 \sqrt [ 3 ] { 4 }$ 
D)  $\sqrt [ 3 ] { 4 }$ 
E)  $- \sqrt [ 3 ] { 4 }$ 
A)  $\sqrt [ 3 ] { 3 } - \sqrt [ 3 ] { 2 }$ 
B)  $- 2 \sqrt [ 3 ] { 4 }$ 
C)  $2 \sqrt [ 3 ] { 4 }$ 
D)  $\sqrt [ 3 ] { 4 }$ 
E)  $- \sqrt [ 3 ] { 4 }$

Question 17

Find the distance between the points (1,-6) and (-7,0).

Accepted Answer

A)  100 
B)  80 
C)  10 
D)  50 
A)  100 
B)  80 
C)  10 
D)  50

Question 18

Simplify: $\sqrt [ 3 ] { - \frac { 27 x ^ { 9 } } { 64 y ^ { 6 } } }$

Accepted Answer

A)  $- \frac { 3 x ^ { 3 } } { 4 y ^ { 2 } }$ 
B)  not a real number 
C)  $- \frac { 3 x ^ { 3 } } { 16 y ^ { 4 } }$ 
D)  $- \frac { 9 x ^ { 3 } } { 16 y ^ { 2 } }$ 
A)  $- \frac { 3 x ^ { 3 } } { 4 y ^ { 2 } }$ 
B)  not a real number 
C)  $- \frac { 3 x ^ { 3 } } { 16 y ^ { 4 } }$ 
D)  $- \frac { 9 x ^ { 3 } } { 16 y ^ { 2 } }$

Question 19

Find the value given that $f ( x ) = \sqrt { x - 2 }$ . $f ( 18 ) =$ __________

Accepted Answer

The answer of Find the value given that \(f (...

Question 20

The base of the 35-foot ladder is 7 feet from the wall. Will the top reach a window ledge that is 34 feet above the ground?
 Verify your result.   Answer yes or no .

Accepted Answer

The answer of The base of the 35-foot ladder is...

Simplify: $\sqrt { - 4 } \cdot \sqrt { - 100 }$

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

Evaluate the expression. $16 ^ { \frac { 1 } { 4 } }$

Simplify the radical expression. All variables represent positive real numbers. $\sqrt [ 3 ] { 625 x ^ { 6 } y ^ { 3 } }$

Simplify by combining like radicals. The variable represents a positive real number. $\sqrt { 216 m } - \sqrt { 192 m } + \sqrt { 588 m }$

Simplify the radical expression. All variables represent positive real numbers. $\sqrt [ 4 ] { 243 x ^ { 12 } y ^ { 4 } }$

Simplify $\sqrt { x ^ { 2 } - 14 x + 49 }$ . Assume all variables are unrestricted and use absolute value symbols when necessary.

In the expression $\sqrt [ 3 ] { 8 x ^ { 6 } }$ , the is 3 and $8 x ^ { 6 }$ is the .

Simplify by combining like radicals. $\sqrt { 98 } - \sqrt { 72 } - \sqrt { 128 }$

Solve: $6 \sqrt { x + 2 } = x - 5$

Simplify the cube root. $\sqrt [ 3 ] { - 8 a ^ { 3 } }$

Radical expressions such as $\sqrt [ 3 ] { 3 }$ and $5 \sqrt [ 3 ] { 3 }$ with the same index and the same radicand are called __________ radicals.

Simplify by combining like radicals. The variable represents a positive real number. $\sqrt [ 3 ] { 54 x } + \sqrt [ 3 ] { 2 x }$

Multiply and simplify, if possible. $( 5 \sqrt { 3 } + 2 ) ( \sqrt { 3 } - 2 )$

Find the domain and range of the function $f ( x )$ . $f ( x ) = \sqrt { x } + 1$

Simplify by combining like radicals. $\sqrt [ 3 ] { 4 } - \sqrt [ 3 ] { 32 }$

Find the distance between the points (1,-6) and (-7,0).

Simplify: $\sqrt [ 3 ] { - \frac { 27 x ^ { 9 } } { 64 y ^ { 6 } } }$

Find the value given that $f ( x ) = \sqrt { x - 2 }$ . $f ( 18 ) =$ __________

The base of the 35-foot ladder is 7 feet from the wall. Will the top reach a window ledge that is 34 feet above the ground? Verify your result. Answer yes or no .

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: −4⋅−100\sqrt { - 4 } \cdot \sqrt { - 100 }−4​⋅−100​

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

Evaluate the expression. 161416 ^ { \frac { 1 } { 4 } }1641​

Simplify the radical expression. All variables represent positive real numbers. 625x6y33\sqrt [ 3 ] { 625 x ^ { 6 } y ^ { 3 } }3625x6y3​

Simplify by combining like radicals. The variable represents a positive real number. 216m−192m+588m\sqrt { 216 m } - \sqrt { 192 m } + \sqrt { 588 m }216m​−192m​+588m​

Simplify the radical expression. All variables represent positive real numbers. 243x12y44\sqrt [ 4 ] { 243 x ^ { 12 } y ^ { 4 } }4243x12y4​

Simplify x2−14x+49\sqrt { x ^ { 2 } - 14 x + 49 }x2−14x+49​ . Assume all variables are unrestricted and use absolute value symbols when necessary.

In the expression 8x63\sqrt [ 3 ] { 8 x ^ { 6 } }38x6​ , the __________ is 3 and 8x68 x ^ { 6 }8x6 is the __________.

Simplify by combining like radicals. 98−72−128\sqrt { 98 } - \sqrt { 72 } - \sqrt { 128 }98​−72​−128​

Solve: 6x+2=x−56 \sqrt { x + 2 } = x - 56x+2​=x−5

Simplify the cube root. −8a33\sqrt [ 3 ] { - 8 a ^ { 3 } }3−8a3​

Radical expressions such as 33\sqrt [ 3 ] { 3 }33​ and 5335 \sqrt [ 3 ] { 3 }533​ with the same index and the same radicand are called __________ radicals.

Simplify by combining like radicals. The variable represents a positive real number. 54x3+2x3\sqrt [ 3 ] { 54 x } + \sqrt [ 3 ] { 2 x }354x​+32x​

Multiply and simplify, if possible. (53+2)(3−2)( 5 \sqrt { 3 } + 2 ) ( \sqrt { 3 } - 2 )(53​+2)(3​−2)

Find the domain and range of the function f(x)f ( x )f(x) . f(x)=x+1f ( x ) = \sqrt { x } + 1f(x)=x​+1

Simplify by combining like radicals. 43−323\sqrt [ 3 ] { 4 } - \sqrt [ 3 ] { 32 }34​−332​

Find the distance between the points (1,-6) and (-7,0).

Simplify: −27x964y63\sqrt [ 3 ] { - \frac { 27 x ^ { 9 } } { 64 y ^ { 6 } } }3−64y627x9​​

Find the value given that f(x)=x−2f ( x ) = \sqrt { x - 2 }f(x)=x−2​ . f(18)=f ( 18 ) =f(18)= __________

The base of the 35-foot ladder is 7 feet from the wall. Will the top reach a window ledge that is 34 feet above the ground? Verify your result. Answer yes or no .

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: $\sqrt { - 4 } \cdot \sqrt { - 100 }$

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

Evaluate the expression. $16 ^ { \frac { 1 } { 4 } }$

Simplify the radical expression. All variables represent positive real numbers. $\sqrt [ 3 ] { 625 x ^ { 6 } y ^ { 3 } }$

Simplify by combining like radicals. The variable represents a positive real number. $\sqrt { 216 m } - \sqrt { 192 m } + \sqrt { 588 m }$

Simplify the radical expression. All variables represent positive real numbers. $\sqrt [ 4 ] { 243 x ^ { 12 } y ^ { 4 } }$

Simplify $\sqrt { x ^ { 2 } - 14 x + 49 }$ . Assume all variables are unrestricted and use absolute value symbols when necessary.

In the expression $\sqrt [ 3 ] { 8 x ^ { 6 } }$ , the is 3 and $8 x ^ { 6 }$ is the .

Simplify by combining like radicals. $\sqrt { 98 } - \sqrt { 72 } - \sqrt { 128 }$

Solve: $6 \sqrt { x + 2 } = x - 5$

Simplify the cube root. $\sqrt [ 3 ] { - 8 a ^ { 3 } }$

Radical expressions such as $\sqrt [ 3 ] { 3 }$ and $5 \sqrt [ 3 ] { 3 }$ with the same index and the same radicand are called __________ radicals.

Simplify by combining like radicals. The variable represents a positive real number. $\sqrt [ 3 ] { 54 x } + \sqrt [ 3 ] { 2 x }$

Multiply and simplify, if possible. $( 5 \sqrt { 3 } + 2 ) ( \sqrt { 3 } - 2 )$

Find the domain and range of the function $f ( x )$ . $f ( x ) = \sqrt { x } + 1$

Simplify by combining like radicals. $\sqrt [ 3 ] { 4 } - \sqrt [ 3 ] { 32 }$

Simplify: $\sqrt [ 3 ] { - \frac { 27 x ^ { 9 } } { 64 y ^ { 6 } } }$

Find the value given that $f ( x ) = \sqrt { x - 2 }$ . $f ( 18 ) =$ __________