Question 1

Simplify the expression. All variables represent positive real numbers. $\left( 25 x ^ { 6 } \right) ^ { \frac { 3 } { 2 } }$

Accepted Answer

$125 x ^ { 9 }$

Question 2

Find the domain of $f ( x ) = \sqrt { x - 7 }$ .

Accepted Answer

A)  $[ 0 , \infty )$ 
B)  $[ - 7 , \infty )$ 
C)  $[ 7 , \infty )$ 
D)  $( - \infty , 7 ) \cup ( 7 , \infty )$ 
A)  $[ 0 , \infty )$ 
B)  $[ - 7 , \infty )$ 
C)  $[ 7 , \infty )$ 
D)  $( - \infty , 7 ) \cup ( 7 , \infty )$ C

Question 3

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

Accepted Answer

A)  $2 + x \sqrt { 7 }$ 
B)  $2 + x + \sqrt { 7 }$ 
C)  $2 x \sqrt { 7 }$ 
D)  $7 x \sqrt { 5 }$ 
E)  $2 \sqrt { 7 x }$ 
A)  $2 + x \sqrt { 7 }$ 
B)  $2 + x + \sqrt { 7 }$ 
C)  $2 x \sqrt { 7 }$ 
D)  $7 x \sqrt { 5 }$ 
E)  $2 \sqrt { 7 x }$ C

Question 4

Find the height h of the ironing board shown in the illustration. Find the exact answer. Then give an approximation to two decimal places.   
Enter your answers without units. Separate the exact answer and approximation with a comma.

Accepted Answer

The answer of Find the height h of the ironing...

Question 5

Multiply and simplify, if possible. $3 \sqrt { 3 } \sqrt { 15 }$

Accepted Answer

A)  $3 \sqrt { 44 }$ 
B)  $3 \sqrt { 5 }$ 
C)  $9 \sqrt { 5 }$ 
D)  $9 \sqrt { 42 }$ 
E)  $3 \sqrt { 43 }$ 
A)  $3 \sqrt { 44 }$ 
B)  $3 \sqrt { 5 }$ 
C)  $9 \sqrt { 5 }$ 
D)  $9 \sqrt { 42 }$ 
E)  $3 \sqrt { 43 }$

Question 6

To __________ the denominator of $\frac { 1 } { \sqrt { 6 } }$ , we multiply the fraction by $\frac { \sqrt { 6 } } { \sqrt { 6 } }$ .

Accepted Answer

A)  simplify 
B)  complicate 
C)  rationalize 
D)  get rid of 
E)  calculate 
A)  simplify 
B)  complicate 
C)  rationalize 
D)  get rid of 
E)  calculate

Question 7

Divide. Write the answer in the form $a + b i$ . $\frac { 65 } { 8 - i }$

Accepted Answer

A)  $4 - 7 i$ 
B)  $6 - i$ 
C)  $8 + i$ 
D)  $6 - 5 i$ 
E)  $8 - 3 i$ 
A)  $4 - 7 i$ 
B)  $6 - i$ 
C)  $8 + i$ 
D)  $6 - 5 i$ 
E)  $8 - 3 i$

Question 8

Solve the equation for the specified variable. $u = \sqrt { 2 g w } \text { for } w$

Accepted Answer

The answer of Solve the equation for the specified variable....

Question 9

Simplify: $\left( \frac { 81 y ^ { 8 } } { 16 } \right) ^ { - \frac { 3 } { 4 } }$

Accepted Answer

A)  $\frac { 64 } { 729 y ^ { 6 } }$ 
B)  $- \frac { 27 y ^ { 6 } } { 8 }$ 
C)  $\frac { 8 } { 27 y ^ { 6 } }$ 
D)  $\frac { 3 y ^ { 2 } } { 2 }$ 
A)  $\frac { 64 } { 729 y ^ { 6 } }$ 
B)  $- \frac { 27 y ^ { 6 } } { 8 }$ 
C)  $\frac { 8 } { 27 y ^ { 6 } }$ 
D)  $\frac { 3 y ^ { 2 } } { 2 }$

Question 10

Find the distance between the pair of points. $( - 6,2 ) , ( - 4 , - 4 )$

Accepted Answer

A)  $2 \sqrt { 10 }$ 
B)  -10 
C)  $2 \sqrt { 11 }$ 
D)  10 
E)  -$2 \sqrt { 10 }$ 
A)  $2 \sqrt { 10 }$ 
B)  -10 
C)  $2 \sqrt { 11 }$ 
D)  10 
E)  -$2 \sqrt { 10 }$

Question 11

Tell why the following expression is not in simplified radical form. Then simplify it. $\frac { 7 } { \sqrt { 2 } }$

Accepted Answer

A radical appears in

Question 12

Simplify the expression. Write the answer without negative exponents. $7 ^ { - \frac { 1 } { 3 } } 7 ^ { - \frac { 5 } { 3 } }$

Accepted Answer

A)  $\frac { 1 } { 49 }$ 
B)  $7 ^ { \frac { 4 } { 3 } }$ 
C)  $\frac { 1 } { 7 ^ { \frac { 2 } { 3 } } }$ 
D)  $7 ^ { \frac { 2 } { 3 } }$ 
E)  49 
A)  $\frac { 1 } { 49 }$ 
B)  $7 ^ { \frac { 4 } { 3 } }$ 
C)  $\frac { 1 } { 7 ^ { \frac { 2 } { 3 } } }$ 
D)  $7 ^ { \frac { 2 } { 3 } }$ 
E)  49

Question 13

Evaluate the square root, if possible, without using a calculator. $\sqrt { - 9 }$

Accepted Answer

A)  2 
B)  3 
C)  -5 
D)  $5 x - 4$ 
E)  not real 
A)  2 
B)  3 
C)  -5 
D)  $5 x - 4$ 
E)  not real

Question 14

$f ( x ) = \sqrt { x }$ and $g ( x ) = \sqrt [ 6 ] { x }$ are __________ functions.

Accepted Answer

The answer of \(f ( x ) = \sqrt {...

Question 15

Solve: $\sqrt { 5 x + 29 } - 4 = 3$

Accepted Answer

The answer of Solve: \(\sqrt { 5 x + 29...

Question 16

Simplify the expression. $\left( - \frac { 8 } { 27 } \right) ^ { - \frac { 4 } { 3 } }$

Accepted Answer

A)  $\frac { 16 } { 81 }$ 
B)  $\frac { 81 } { 16 }$ 
C)  $\frac { 2 } { 3 }$ 
D)  $\left( \frac { 3 } { 2 } \right) ^ { 4 }$ 
E)  $\frac { 3 } { 2 }$ 
A)  $\frac { 16 } { 81 }$ 
B)  $\frac { 81 } { 16 }$ 
C)  $\frac { 2 } { 3 }$ 
D)  $\left( \frac { 3 } { 2 } \right) ^ { 4 }$ 
E)  $\frac { 3 } { 2 }$

Question 17

Solve: $\sqrt [ 3 ] { 4 x + 9 } = - 3$

Accepted Answer

The answer of Solve: \(\sqrt [ 3 ] { 4...

Question 18

Multiply. Write the answer in the form $a + b i$ . $- 3 i ( 6 - 6 i )$

Accepted Answer

A)  $- 10 - 10 i$ 
B)  $14 - 14 i$ 
C)  $16 - 16 i$ 
D)  $- 12 + 12 i$ 
E)  $- 18 - 18 i$ 
A)  $- 10 - 10 i$ 
B)  $14 - 14 i$ 
C)  $16 - 16 i$ 
D)  $- 12 + 12 i$ 
E)  $- 18 - 18 i$

Question 19

Rationalize the denominator. $\frac { 4 } { \sqrt [ 3 ] { 16 } }$

Accepted Answer

The answer of Rationalize the denominator. \(\frac { 4 }...

Question 20

Square both sides of the equation $\sqrt { y + 5 } = \sqrt { 5 y + 2 } - 2$ and then simplify.

Accepted Answer

A)  $y + 5 = 5 y + 6$ 
B)  $y + 5 = 5 y + 6 - \sqrt { 5 y + 2 }$ 
C)  $y + 5 = 5 y + 6 - 4 \sqrt { 5 y + 2 }$ 
D)  $y + 5 = 5 y$ 
A)  $y + 5 = 5 y + 6$ 
B)  $y + 5 = 5 y + 6 - \sqrt { 5 y + 2 }$ 
C)  $y + 5 = 5 y + 6 - 4 \sqrt { 5 y + 2 }$ 
D)  $y + 5 = 5 y$

Simplify the expression. All variables represent positive real numbers. $\left( 25 x ^ { 6 } \right) ^ { \frac { 3 } { 2 } }$

Find the domain of $f ( x ) = \sqrt { x - 7 }$ .

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

Find the height h of the ironing board shown in the illustration. Find the exact answer. Then give an approximation to two decimal places. Enter your answers without units. Separate the exact answer and approximation with a comma.

Multiply and simplify, if possible. $3 \sqrt { 3 } \sqrt { 15 }$

To __________ the denominator of $\frac { 1 } { \sqrt { 6 } }$ , we multiply the fraction by $\frac { \sqrt { 6 } } { \sqrt { 6 } }$ .

Divide. Write the answer in the form $a + b i$ . $\frac { 65 } { 8 - i }$

Solve the equation for the specified variable. $u = \sqrt { 2 g w } \text { for } w$

Simplify: $\left( \frac { 81 y ^ { 8 } } { 16 } \right) ^ { - \frac { 3 } { 4 } }$

Find the distance between the pair of points. $( - 6,2 ) , ( - 4 , - 4 )$

Tell why the following expression is not in simplified radical form. Then simplify it. $\frac { 7 } { \sqrt { 2 } }$

Simplify the expression. Write the answer without negative exponents. $7 ^ { - \frac { 1 } { 3 } } 7 ^ { - \frac { 5 } { 3 } }$

Evaluate the square root, if possible, without using a calculator. $\sqrt { - 9 }$

$f ( x ) = \sqrt { x }$ and $g ( x ) = \sqrt [ 6 ] { x }$ are __________ functions.

Solve: $\sqrt { 5 x + 29 } - 4 = 3$

Simplify the expression. $\left( - \frac { 8 } { 27 } \right) ^ { - \frac { 4 } { 3 } }$

Solve: $\sqrt [ 3 ] { 4 x + 9 } = - 3$

Multiply. Write the answer in the form $a + b i$ . $- 3 i ( 6 - 6 i )$

Rationalize the denominator. $\frac { 4 } { \sqrt [ 3 ] { 16 } }$

Square both sides of the equation $\sqrt { y + 5 } = \sqrt { 5 y + 2 } - 2$ and then simplify.

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 expression. All variables represent positive real numbers. (25x6)32\left( 25 x ^ { 6 } \right) ^ { \frac { 3 } { 2 } }(25x6)23​

Find the domain of f(x)=x−7f ( x ) = \sqrt { x - 7 }f(x)=x−7​ .

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

Find the height h of the ironing board shown in the illustration. Find the exact answer. Then give an approximation to two decimal places. Enter your answers without units. Separate the exact answer and approximation with a comma.

Multiply and simplify, if possible. 33153 \sqrt { 3 } \sqrt { 15 }33​15​

To __________ the denominator of 16\frac { 1 } { \sqrt { 6 } }6​1​ , we multiply the fraction by 66\frac { \sqrt { 6 } } { \sqrt { 6 } }6​6​​ .

Divide. Write the answer in the form a+bia + b ia+bi . 658−i\frac { 65 } { 8 - i }8−i65​

Solve the equation for the specified variable. u=2gw for wu = \sqrt { 2 g w } \text { for } wu=2gw​ for w

Simplify: (81y816)−34\left( \frac { 81 y ^ { 8 } } { 16 } \right) ^ { - \frac { 3 } { 4 } }(1681y8​)−43​

Find the distance between the pair of points. (−6,2),(−4,−4)( - 6,2 ) , ( - 4 , - 4 )(−6,2),(−4,−4)

Tell why the following expression is not in simplified radical form. Then simplify it. 72\frac { 7 } { \sqrt { 2 } }2​7​

Simplify the expression. Write the answer without negative exponents. 7−137−537 ^ { - \frac { 1 } { 3 } } 7 ^ { - \frac { 5 } { 3 } }7−31​7−35​

Evaluate the square root, if possible, without using a calculator. −9\sqrt { - 9 }−9​

f(x)=xf ( x ) = \sqrt { x }f(x)=x​ and g(x)=x6g ( x ) = \sqrt [ 6 ] { x }g(x)=6x​ are __________ functions.

Solve: 5x+29−4=3\sqrt { 5 x + 29 } - 4 = 35x+29​−4=3

Simplify the expression. (−827)−43\left( - \frac { 8 } { 27 } \right) ^ { - \frac { 4 } { 3 } }(−278​)−34​

Solve: 4x+93=−3\sqrt [ 3 ] { 4 x + 9 } = - 334x+9​=−3

Multiply. Write the answer in the form a+bia + b ia+bi . −3i(6−6i)- 3 i ( 6 - 6 i )−3i(6−6i)

Rationalize the denominator. 4163\frac { 4 } { \sqrt [ 3 ] { 16 } }316​4​

Square both sides of the equation y+5=5y+2−2\sqrt { y + 5 } = \sqrt { 5 y + 2 } - 2y+5​=5y+2​−2 and then simplify.

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 expression. All variables represent positive real numbers. $\left( 25 x ^ { 6 } \right) ^ { \frac { 3 } { 2 } }$

Find the domain of $f ( x ) = \sqrt { x - 7 }$ .

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

Multiply and simplify, if possible. $3 \sqrt { 3 } \sqrt { 15 }$

To __________ the denominator of $\frac { 1 } { \sqrt { 6 } }$ , we multiply the fraction by $\frac { \sqrt { 6 } } { \sqrt { 6 } }$ .

Divide. Write the answer in the form $a + b i$ . $\frac { 65 } { 8 - i }$

Solve the equation for the specified variable. $u = \sqrt { 2 g w } \text { for } w$

Simplify: $\left( \frac { 81 y ^ { 8 } } { 16 } \right) ^ { - \frac { 3 } { 4 } }$

Find the distance between the pair of points. $( - 6,2 ) , ( - 4 , - 4 )$

Tell why the following expression is not in simplified radical form. Then simplify it. $\frac { 7 } { \sqrt { 2 } }$

Simplify the expression. Write the answer without negative exponents. $7 ^ { - \frac { 1 } { 3 } } 7 ^ { - \frac { 5 } { 3 } }$

Evaluate the square root, if possible, without using a calculator. $\sqrt { - 9 }$

$f ( x ) = \sqrt { x }$ and $g ( x ) = \sqrt [ 6 ] { x }$ are __________ functions.

Solve: $\sqrt { 5 x + 29 } - 4 = 3$

Simplify the expression. $\left( - \frac { 8 } { 27 } \right) ^ { - \frac { 4 } { 3 } }$

Solve: $\sqrt [ 3 ] { 4 x + 9 } = - 3$

Multiply. Write the answer in the form $a + b i$ . $- 3 i ( 6 - 6 i )$

Rationalize the denominator. $\frac { 4 } { \sqrt [ 3 ] { 16 } }$

Square both sides of the equation $\sqrt { y + 5 } = \sqrt { 5 y + 2 } - 2$ and then simplify.