Question 1

Express the number in terms of $i$ . $\sqrt { - 4 }$

Accepted Answer

The answer of Express the number in terms of $i$...

Question 2

Perform the indicated operation. $5 ^ { - \frac { 4 } { 3 } } \cdot 5 ^ { \frac { 5 } { 6 } }$

Accepted Answer

A)  $\frac { 1 } { 25 ^ { \frac { 1 } { 2 } } }$ 
B)  $\frac { 1 } { 5 ^ { \frac { 1 } { 2 } } }$ 
C)  $25 ^ { \frac { 1 } { 2 } }$ 
D)  $5 ^ { \frac { 1 } { 2 } }$ 
A)  $\frac { 1 } { 25 ^ { \frac { 1 } { 2 } } }$ 
B)  $\frac { 1 } { 5 ^ { \frac { 1 } { 2 } } }$ 
C)  $25 ^ { \frac { 1 } { 2 } }$ 
D)  $5 ^ { \frac { 1 } { 2 } }$

Question 3

Evaluate the square root, if possible, without using a calculator. $\sqrt { \frac { 1 } { 36 } }$

Accepted Answer

The answer of Evaluate the square root, if possible, without...

Question 4

Simplify $( 3 + 2 i ) ^ { - 2 }$ and write the result in the form a+bi

Accepted Answer

The answer of Simplify \(( 3 + 2 i )...

Question 5

Once a radical is isolated in a radical equation, the next step is to raise each side to the same power as the ________ of the radical.

Accepted Answer

The answer of Once a radical is isolated in a...

Question 6

The __________ of $\sqrt { x } + 6$ is $\sqrt { x } - 6$ .

Accepted Answer

A)  conjugate 
B)  conjoined 
C)  related 
D)  couple 
E)  connector 
A)  conjugate 
B)  conjoined 
C)  related 
D)  couple 
E)  connector

Question 7

Evaluate the square root, if possible, without using a calculator. $\sqrt { 121 }$

Accepted Answer

The answer of Evaluate the square root, if possible, without...

Question 8

The lengths of two sides of the right triangle ABC are given. Find the length of the missing side. a=12 ft and b=16 ft

Accepted Answer

A)  20 ft 
B)  28 ft 
C)  $28 \sqrt { 2 }$ ft 
D)  4 ft 
E)  5 ft 
A)  20 ft 
B)  28 ft 
C)  $28 \sqrt { 2 }$ ft 
D)  4 ft 
E)  5 ft

Question 9

Simplify the radical expression. All variables represent positive real numbers. $\sqrt [ 4 ] { 243 x ^ { 8 } y ^ { 4 } }$

Accepted Answer

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

Question 10

Simplify by combining like radicals. $\sqrt { 3 } + \sqrt { 27 }$

Accepted Answer

A)  3 
B)  $4 \sqrt { 3 }$ 
C)  $9 \sqrt { 3 }$ 
D)  9 
E)  $3 \sqrt { 3 }$ 
A)  3 
B)  $4 \sqrt { 3 }$ 
C)  $9 \sqrt { 3 }$ 
D)  9 
E)  $3 \sqrt { 3 }$

Question 11

The graph of a square root function $f$ is shown below.  
 Find the value(s) of x for which $f ( x ) = 1$ .

Accepted Answer

A)  x=3 
B)  x=6 
C)  x=5 
D)  $x = 4$ 
E)  $x = 2$ 
A)  x=3 
B)  x=6 
C)  x=5 
D)  $x = 4$ 
E)  $x = 2$

Question 12

Find the missing side lengths in each triangle. Give the exact answer and then an approximation to two decimal places, when appropriate.

Accepted Answer

A)  $x = 4 , h = 5$ 
B)  $x = 5 , h = 5 \sqrt { 2 } \approx 5.66$ 
C)  $x = 4 \sqrt { 2 } \approx 5.66 , h = 4$ 
D)  $x = 4 , h = 4 \sqrt { 2 } \approx 5.71$ 
E)  $x = 4 , h = 4 \sqrt { 2 } \approx 5.66$ 
A)  $x = 4 , h = 5$ 
B)  $x = 5 , h = 5 \sqrt { 2 } \approx 5.66$ 
C)  $x = 4 \sqrt { 2 } \approx 5.66 , h = 4$ 
D)  $x = 4 , h = 4 \sqrt { 2 } \approx 5.71$ 
E)  $x = 4 , h = 4 \sqrt { 2 } \approx 5.66$

Question 13

Simplify: $\frac { \sqrt { 96 x ^ { 5 } } } { \sqrt { 2 x } }$ . Assume all variables are positive.

Accepted Answer

The answer of Simplify: \(\frac { \sqrt { 96 x...

Question 14

Find the missing side lengths in the triangle. Give the exact answer and then an approximation to two decimal places, when appropriate.

Accepted Answer

A)  $x = 10 \sqrt { 3 } \approx 17.35 , h = 20$ 
B)  $x = 10 \sqrt { 3 } \approx 17.32 , h = 20$ 
C)  $x = 20 , h = 10 \sqrt { 3 } \approx 17.32$ 
D)  $x = 21 , h = 10 \sqrt { 3 } \approx 17.35$ 
E)  $x = 10 \sqrt { 3 } \approx 17.32 , h = 21$ 
A)  $x = 10 \sqrt { 3 } \approx 17.35 , h = 20$ 
B)  $x = 10 \sqrt { 3 } \approx 17.32 , h = 20$ 
C)  $x = 20 , h = 10 \sqrt { 3 } \approx 17.32$ 
D)  $x = 21 , h = 10 \sqrt { 3 } \approx 17.35$ 
E)  $x = 10 \sqrt { 3 } \approx 17.32 , h = 21$

Question 15

Evaluate the expression. $( - 64 ) ^ { \frac { 1 } { 3 } }$

Accepted Answer

The answer of Evaluate the expression. \(( - 64 )...

Question 16

Find the distance between the pair of points. $( 0,0 ) , ( 6 , - 8 )$

Accepted Answer

A)  6 
B)  9 
C)  7 
D)  8 
E)  10 
A)  6 
B)  9 
C)  7 
D)  8 
E)  10

Question 17

Simplify the expression. $\sqrt { 27 }$

Accepted Answer

The answer of Simplify the expression. $\sqrt { 27 }$...

Question 18

Simplify by combining like radicals. The variable represents a positive real number. $4 \sqrt { 2 x } + 6 \sqrt { 2 x }$

Accepted Answer

A)  $10 \sqrt { x }$ 
B)  $10 \sqrt { 2 x }$ 
C)  $2 \sqrt { 2 x }$ 
D)  $24 \sqrt { 2 x }$ 
E)  $20 \sqrt { x }$ 
A)  $10 \sqrt { x }$ 
B)  $10 \sqrt { 2 x }$ 
C)  $2 \sqrt { 2 x }$ 
D)  $24 \sqrt { 2 x }$ 
E)  $20 \sqrt { x }$

Question 19

Multiply and simplify, if possible. All variables represent positive real numbers. $( \sqrt { 5 m } + \sqrt { 2 n } ) ( \sqrt { 5 m } - \sqrt { 2 n } )$

Accepted Answer

A)  $5 m - 2 n$ 
B)  $5 n - 2 m$ 
C)  $- 5 m - 2 n$ 
D)  $5 m + 2 n$ 
E)  $- 5 m + 2 n$ 
A)  $5 m - 2 n$ 
B)  $5 n - 2 m$ 
C)  $- 5 m - 2 n$ 
D)  $5 m + 2 n$ 
E)  $- 5 m + 2 n$

Question 20

Simplify the radical expression. $\sqrt { 640 }$

Accepted Answer

The answer of Simplify the radical expression. \(\sqrt { 640...

Express the number in terms of $i$ . $\sqrt { - 4 }$

Perform the indicated operation. $5 ^ { - \frac { 4 } { 3 } } \cdot 5 ^ { \frac { 5 } { 6 } }$

Evaluate the square root, if possible, without using a calculator. $\sqrt { \frac { 1 } { 36 } }$

Simplify $( 3 + 2 i ) ^ { - 2 }$ and write the result in the form a+bi

Once a radical is isolated in a radical equation, the next step is to raise each side to the same power as the ________ of the radical.

The __________ of $\sqrt { x } + 6$ is $\sqrt { x } - 6$ .

Evaluate the square root, if possible, without using a calculator. $\sqrt { 121 }$

The lengths of two sides of the right triangle ABC are given. Find the length of the missing side. a=12 ft and b=16 ft

Simplify the radical expression. All variables represent positive real numbers. $\sqrt [ 4 ] { 243 x ^ { 8 } y ^ { 4 } }$

Simplify by combining like radicals. $\sqrt { 3 } + \sqrt { 27 }$

The graph of a square root function $f$ is shown below. Find the value(s) of x for which $f ( x ) = 1$ .

Find the missing side lengths in each triangle. Give the exact answer and then an approximation to two decimal places, when appropriate.

Simplify: $\frac { \sqrt { 96 x ^ { 5 } } } { \sqrt { 2 x } }$ . Assume all variables are positive.

Find the missing side lengths in the triangle. Give the exact answer and then an approximation to two decimal places, when appropriate.

Evaluate the expression. $( - 64 ) ^ { \frac { 1 } { 3 } }$

Find the distance between the pair of points. $( 0,0 ) , ( 6 , - 8 )$

Simplify the expression. $\sqrt { 27 }$

Simplify by combining like radicals. The variable represents a positive real number. $4 \sqrt { 2 x } + 6 \sqrt { 2 x }$

Multiply and simplify, if possible. All variables represent positive real numbers. $( \sqrt { 5 m } + \sqrt { 2 n } ) ( \sqrt { 5 m } - \sqrt { 2 n } )$

Simplify the radical expression. $\sqrt { 640 }$

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

Express the number in terms of iii . −4\sqrt { - 4 }−4​

Perform the indicated operation. 5−43⋅5565 ^ { - \frac { 4 } { 3 } } \cdot 5 ^ { \frac { 5 } { 6 } }5−34​⋅565​

Evaluate the square root, if possible, without using a calculator. 136\sqrt { \frac { 1 } { 36 } }361​​

Simplify (3+2i)−2( 3 + 2 i ) ^ { - 2 }(3+2i)−2 and write the result in the form a+bi

Once a radical is isolated in a radical equation, the next step is to raise each side to the same power as the ________ of the radical.

The __________ of x+6\sqrt { x } + 6x​+6 is x−6\sqrt { x } - 6x​−6 .

Evaluate the square root, if possible, without using a calculator. 121\sqrt { 121 }121​

The lengths of two sides of the right triangle ABC are given. Find the length of the missing side. a=12 ft and b=16 ft

Simplify the radical expression. All variables represent positive real numbers. 243x8y44\sqrt [ 4 ] { 243 x ^ { 8 } y ^ { 4 } }4243x8y4​

Simplify by combining like radicals. 3+27\sqrt { 3 } + \sqrt { 27 }3​+27​

The graph of a square root function fff is shown below. Find the value(s) of x for which f(x)=1f ( x ) = 1f(x)=1 .

Find the missing side lengths in each triangle. Give the exact answer and then an approximation to two decimal places, when appropriate.

Simplify: 96x52x\frac { \sqrt { 96 x ^ { 5 } } } { \sqrt { 2 x } }2x​96x5​​ . Assume all variables are positive.

Find the missing side lengths in the triangle. Give the exact answer and then an approximation to two decimal places, when appropriate.

Evaluate the expression. (−64)13( - 64 ) ^ { \frac { 1 } { 3 } }(−64)31​

Find the distance between the pair of points. (0,0),(6,−8)( 0,0 ) , ( 6 , - 8 )(0,0),(6,−8)

Simplify the expression. 27\sqrt { 27 }27​

Simplify by combining like radicals. The variable represents a positive real number. 42x+62x4 \sqrt { 2 x } + 6 \sqrt { 2 x }42x​+62x​

Multiply and simplify, if possible. All variables represent positive real numbers. (5m+2n)(5m−2n)( \sqrt { 5 m } + \sqrt { 2 n } ) ( \sqrt { 5 m } - \sqrt { 2 n } )(5m​+2n​)(5m​−2n​)

Simplify the radical expression. 640\sqrt { 640 }640​

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

Express the number in terms of $i$ . $\sqrt { - 4 }$

Perform the indicated operation. $5 ^ { - \frac { 4 } { 3 } } \cdot 5 ^ { \frac { 5 } { 6 } }$

Evaluate the square root, if possible, without using a calculator. $\sqrt { \frac { 1 } { 36 } }$

Simplify $( 3 + 2 i ) ^ { - 2 }$ and write the result in the form a+bi

The __________ of $\sqrt { x } + 6$ is $\sqrt { x } - 6$ .

Evaluate the square root, if possible, without using a calculator. $\sqrt { 121 }$

Simplify the radical expression. All variables represent positive real numbers. $\sqrt [ 4 ] { 243 x ^ { 8 } y ^ { 4 } }$

Simplify by combining like radicals. $\sqrt { 3 } + \sqrt { 27 }$

The graph of a square root function $f$ is shown below. Find the value(s) of x for which $f ( x ) = 1$ .

Simplify: $\frac { \sqrt { 96 x ^ { 5 } } } { \sqrt { 2 x } }$ . Assume all variables are positive.

Evaluate the expression. $( - 64 ) ^ { \frac { 1 } { 3 } }$

Find the distance between the pair of points. $( 0,0 ) , ( 6 , - 8 )$

Simplify the expression. $\sqrt { 27 }$

Simplify by combining like radicals. The variable represents a positive real number. $4 \sqrt { 2 x } + 6 \sqrt { 2 x }$

Multiply and simplify, if possible. All variables represent positive real numbers. $( \sqrt { 5 m } + \sqrt { 2 n } ) ( \sqrt { 5 m } - \sqrt { 2 n } )$

Simplify the radical expression. $\sqrt { 640 }$