Question 1

In a right triangle, the side opposite the 90∘ angle is called the __________.

Accepted Answer

A)  right angle 
B)  hypotenuse 
C)  leg 
D)  opposite side 
A)  right angle 
B)  hypotenuse 
C)  leg 
D)  opposite side

Question 2

Simplify $\sqrt { 25 a ^ { 30 } + 40 a ^ { 15 } b ^ { 14 } + 16 b ^ { 28 } }$ and assume that a 0 and b 0.

Accepted Answer

The answer of Simplify \(\sqrt { 25 a ^ {...

Question 3

In the exponential expression $48 ^ { \frac { 5 } { 4 } }$ , 48 is the __________ and $\frac { 5 } { 4 }$ is the __________.

Accepted Answer

A)  radicand, power 
B)  index, radicand 
C)  base, exponent 
D)  index, root 
E)  power, root 
A)  radicand, power 
B)  index, radicand 
C)  base, exponent 
D)  index, root 
E)  power, root

Question 4

Simplify: $i ^ { 26 }$

Accepted Answer

The answer of Simplify: $i ^ { 26 }$...

Question 5

Multiply and simplify, if possible. $( \sqrt { 5 } + 2 ) ( \sqrt { 5 } - 6 )$

Accepted Answer

A)  $4 + 7 \sqrt { 5 }$ 
B)  $7 + 4 \sqrt { 5 }$ 
C)  $7 - 4 \sqrt { 5 }$ 
D)  $- 7 - 4 \sqrt { 5 }$ 
E)  $- 7 + 4 \sqrt { 5 }$ 
A)  $4 + 7 \sqrt { 5 }$ 
B)  $7 + 4 \sqrt { 5 }$ 
C)  $7 - 4 \sqrt { 5 }$ 
D)  $- 7 - 4 \sqrt { 5 }$ 
E)  $- 7 + 4 \sqrt { 5 }$

Question 6

Perform the operation. Write the answer in the form $a + b i$ . $( 7 - 4 i ) - ( 3 + 2 i )$

Accepted Answer

The answer of Perform the operation. Write the answer in...

Question 7

The number 121 has two square roots. The positive or __________ square root of 121 is 11.

Accepted Answer

The answer of The number 121 has two square roots....

Question 8

A __________ number is any number that can be written in the form a+bi , where a and b are real numbers and $i = \sqrt { - 1 }$ .

Accepted Answer

The answer of A __________ number is any number that...

Question 9

Perform the operation. Write the answer without negative exponents. $\frac { 5 ^ { - \frac { 1 } { 5 } } \cdot 5 ^ { \frac { 4 } { 5 } } } { 5 ^ { \frac { 7 } { 5 } } }$

Accepted Answer

A)  $\frac { 1 } { 25 ^ { \frac { 3 } { 5 } } }$ 
B)  $5 ^ { \frac { 4 } { 5 } }$ 
C)  $\frac { 1 } { 5 }$ 
D)  $\frac { 1 } { 5 ^ { \frac { 4 } { 5 } } }$ 
A)  $\frac { 1 } { 25 ^ { \frac { 3 } { 5 } } }$ 
B)  $5 ^ { \frac { 4 } { 5 } }$ 
C)  $\frac { 1 } { 5 }$ 
D)  $\frac { 1 } { 5 ^ { \frac { 4 } { 5 } } }$

Question 10

Simplify the radical expression. All variables represent positive real numbers. $\sqrt { 112 a ^ { 2 } b ^ { 3 } }$

Accepted Answer

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

Question 11

The formula to find the distance d between two points $\left( x _ { 1 } , y _ { 1 } \right)$ and $\left( x _ { 2 } , y _ { 2 } \right)$ is d= __________.

Accepted Answer

The answer of The formula to find the distance d...

Question 12

Simplify the radical, if possible. $\sqrt [ 4 ] { - 81 }$

Accepted Answer

The answer of Simplify the radical, if possible. \(\sqrt [...

Question 13

When solving equations containing radicals, try to __________.

Accepted Answer

A)  collect like terms 
B)  isolate one radical expression on one side of the equation 
C)  subtract one radical expression from another radical expression 
D)  isolate radical expressions on one side of the equation 
E)  add one radical expression to another radical expression 
A)  collect like terms 
B)  isolate one radical expression on one side of the equation 
C)  subtract one radical expression from another radical expression 
D)  isolate radical expressions on one side of the equation 
E)  add one radical expression to another radical expression

Question 14

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

Accepted Answer

A)  $12 + 5 i$ 
B)  $16 + 21 i$ 
C)  $14 - 2 i$ 
D)  $18 - 2 i$ 
E)  $20 + 21 i$ 
A)  $12 + 5 i$ 
B)  $16 + 21 i$ 
C)  $14 - 2 i$ 
D)  $18 - 2 i$ 
E)  $20 + 21 i$

Question 15

Simplify the expression. $\sqrt [ 3 ] { 108 }$

Accepted Answer

A)  $4 \sqrt [ 3 ] { 4 }$ 
B)  $3 \sqrt [ 3 ] { 4 }$ 
C)  $4 + \sqrt [ 3 ] { 4 }$ 
D)  12 
E)  $4 + \sqrt [ 3 ] { 3 }$ 
A)  $4 \sqrt [ 3 ] { 4 }$ 
B)  $3 \sqrt [ 3 ] { 4 }$ 
C)  $4 + \sqrt [ 3 ] { 4 }$ 
D)  12 
E)  $4 + \sqrt [ 3 ] { 3 }$

Question 16

Multiply. $\sqrt { - 16 } \sqrt { - 64 }$

Accepted Answer

The answer of Multiply. \(\sqrt { - 16 } \sqrt...

Question 17

Multiply and simplify, if possible. $9 \sqrt { m n ^ { 9 } } ( 6 \sqrt { m n } )$

Accepted Answer

A)  $54 \mathrm { mn } { } ^ { 5 }$ 
B)  $15 m \sqrt { n } 10$ 
C)  $15 n ^ { 5 } \sqrt { m }$ 
D)  $54 m ^ { 2 } n ^ { 5 }$ 
E)  $54 m \sqrt { n ^ { 9 } }$ 
A)  $54 \mathrm { mn } { } ^ { 5 }$ 
B)  $15 m \sqrt { n } 10$ 
C)  $15 n ^ { 5 } \sqrt { m }$ 
D)  $54 m ^ { 2 } n ^ { 5 }$ 
E)  $54 m \sqrt { n ^ { 9 } }$

Question 18

Simplify $\frac { 10 } { \sqrt [ 3 ] { 100 } }$ by rationalizing the denominator.

Accepted Answer

A)  $\frac { \sqrt [ 3 ] { 100 } } { 10 }$ 
B)  $\frac { \sqrt [ 3 ] { 10 } } { 10 }$ 
C)  $\sqrt [ 3 ] { 10 }$ 
D)  3 $10 \sqrt [ 3 ] { 10 }$ 
A)  $\frac { \sqrt [ 3 ] { 100 } } { 10 }$ 
B)  $\frac { \sqrt [ 3 ] { 10 } } { 10 }$ 
C)  $\sqrt [ 3 ] { 10 }$ 
D)  3 $10 \sqrt [ 3 ] { 10 }$

Question 19

Use rational exponents to simplify the radical. $\sqrt [ 6 ] { \sqrt { x } }$

Accepted Answer

The answer of Use rational exponents to simplify the radical....

Question 20

Divide. Write the answer in the form $a + b i$ . $\frac { 3 + 4 i } { 3 + i }$

Accepted Answer

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

In a right triangle, the side opposite the 90^∘ angle is called the __________.

Simplify $\sqrt { 25 a ^ { 30 } + 40 a ^ { 15 } b ^ { 14 } + 16 b ^ { 28 } }$ and assume that a 0 and b 0.

In the exponential expression $48 ^ { \frac { 5 } { 4 } }$ , 48 is the and $\frac { 5 } { 4 }$ is the .

Simplify: $i ^ { 26 }$

Multiply and simplify, if possible. $( \sqrt { 5 } + 2 ) ( \sqrt { 5 } - 6 )$

Perform the operation. Write the answer in the form $a + b i$ . $( 7 - 4 i ) - ( 3 + 2 i )$

The number 121 has two square roots. The positive or __________ square root of 121 is 11.

A __________ number is any number that can be written in the form a+bi , where a and b are real numbers and $i = \sqrt { - 1 }$ .

Perform the operation. Write the answer without negative exponents. $\frac { 5 ^ { - \frac { 1 } { 5 } } \cdot 5 ^ { \frac { 4 } { 5 } } } { 5 ^ { \frac { 7 } { 5 } } }$

Simplify the radical expression. All variables represent positive real numbers. $\sqrt { 112 a ^ { 2 } b ^ { 3 } }$

The formula to find the distance d between two points $\left( x _ { 1 } , y _ { 1 } \right)$ and $\left( x _ { 2 } , y _ { 2 } \right)$ is d= __________.

Simplify the radical, if possible. $\sqrt [ 4 ] { - 81 }$

When solving equations containing radicals, try to __________.

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

Simplify the expression. $\sqrt [ 3 ] { 108 }$

Multiply. $\sqrt { - 16 } \sqrt { - 64 }$

Multiply and simplify, if possible. $9 \sqrt { m n ^ { 9 } } ( 6 \sqrt { m n } )$

Simplify $\frac { 10 } { \sqrt [ 3 ] { 100 } }$ by rationalizing the denominator.

Use rational exponents to simplify the radical. $\sqrt [ 6 ] { \sqrt { x } }$

Divide. Write the answer in the form $a + b i$ . $\frac { 3 + 4 i } { 3 + i }$

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

In a right triangle, the side opposite the 90∘ angle is called the __________.

Simplify 25a30+40a15b14+16b28\sqrt { 25 a ^ { 30 } + 40 a ^ { 15 } b ^ { 14 } + 16 b ^ { 28 } }25a30+40a15b14+16b28​ and assume that a 0 and b 0.

In the exponential expression 485448 ^ { \frac { 5 } { 4 } }4845​ , 48 is the __________ and 54\frac { 5 } { 4 }45​ is the __________.

Simplify: i26i ^ { 26 }i26

Multiply and simplify, if possible. (5+2)(5−6)( \sqrt { 5 } + 2 ) ( \sqrt { 5 } - 6 )(5​+2)(5​−6)

Perform the operation. Write the answer in the form a+bia + b ia+bi . (7−4i)−(3+2i)( 7 - 4 i ) - ( 3 + 2 i )(7−4i)−(3+2i)

The number 121 has two square roots. The positive or __________ square root of 121 is 11.

A __________ number is any number that can be written in the form a+bi , where a and b are real numbers and i=−1i = \sqrt { - 1 }i=−1​ .

Perform the operation. Write the answer without negative exponents. 5−15⋅545575\frac { 5 ^ { - \frac { 1 } { 5 } } \cdot 5 ^ { \frac { 4 } { 5 } } } { 5 ^ { \frac { 7 } { 5 } } }557​5−51​⋅554​​

Simplify the radical expression. All variables represent positive real numbers. 112a2b3\sqrt { 112 a ^ { 2 } b ^ { 3 } }112a2b3​

The formula to find the distance d between two points (x1,y1)\left( x _ { 1 } , y _ { 1 } \right)(x1​,y1​) and (x2,y2)\left( x _ { 2 } , y _ { 2 } \right)(x2​,y2​) is d= __________.

Simplify the radical, if possible. −814\sqrt [ 4 ] { - 81 }4−81​

When solving equations containing radicals, try to __________.

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

Simplify the expression. 1083\sqrt [ 3 ] { 108 }3108​

Multiply. −16−64\sqrt { - 16 } \sqrt { - 64 }−16​−64​

Multiply and simplify, if possible. 9mn9(6mn)9 \sqrt { m n ^ { 9 } } ( 6 \sqrt { m n } )9mn9​(6mn​)

Simplify 101003\frac { 10 } { \sqrt [ 3 ] { 100 } }3100​10​ by rationalizing the denominator.

Use rational exponents to simplify the radical. x6\sqrt [ 6 ] { \sqrt { x } }6x​​

Divide. Write the answer in the form a+bia + b ia+bi . 3+4i3+i\frac { 3 + 4 i } { 3 + i }3+i3+4i​

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

In a right triangle, the side opposite the 90^∘ angle is called the __________.

Simplify $\sqrt { 25 a ^ { 30 } + 40 a ^ { 15 } b ^ { 14 } + 16 b ^ { 28 } }$ and assume that a 0 and b 0.

In the exponential expression $48 ^ { \frac { 5 } { 4 } }$ , 48 is the and $\frac { 5 } { 4 }$ is the .

Simplify: $i ^ { 26 }$

Multiply and simplify, if possible. $( \sqrt { 5 } + 2 ) ( \sqrt { 5 } - 6 )$

Perform the operation. Write the answer in the form $a + b i$ . $( 7 - 4 i ) - ( 3 + 2 i )$

A __________ number is any number that can be written in the form a+bi , where a and b are real numbers and $i = \sqrt { - 1 }$ .

Perform the operation. Write the answer without negative exponents. $\frac { 5 ^ { - \frac { 1 } { 5 } } \cdot 5 ^ { \frac { 4 } { 5 } } } { 5 ^ { \frac { 7 } { 5 } } }$

Simplify the radical expression. All variables represent positive real numbers. $\sqrt { 112 a ^ { 2 } b ^ { 3 } }$

The formula to find the distance d between two points $\left( x _ { 1 } , y _ { 1 } \right)$ and $\left( x _ { 2 } , y _ { 2 } \right)$ is d= __________.

Simplify the radical, if possible. $\sqrt [ 4 ] { - 81 }$

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

Simplify the expression. $\sqrt [ 3 ] { 108 }$

Multiply. $\sqrt { - 16 } \sqrt { - 64 }$

Multiply and simplify, if possible. $9 \sqrt { m n ^ { 9 } } ( 6 \sqrt { m n } )$

Simplify $\frac { 10 } { \sqrt [ 3 ] { 100 } }$ by rationalizing the denominator.

Use rational exponents to simplify the radical. $\sqrt [ 6 ] { \sqrt { x } }$

Divide. Write the answer in the form $a + b i$ . $\frac { 3 + 4 i } { 3 + i }$