Question 1

Find the distance between the pair of points. $( - 1 , - 1 ) , ( 7,5 )$

Accepted Answer

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

Question 2

Rationalize the denominator. $\frac { \sqrt { 3 } + \sqrt { 2 } } { \sqrt { 3 } - \sqrt { 2 } }$

Accepted Answer

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

Question 3

The lengths of two sides of the right triangle ABC are given. Find the length of the missing side. $b = 24$ ft and 145 ft

Accepted Answer

A)  143 ft 
B)  121 ft 
C)  141 ft 
D)  142 ft 
E)  140 ft 
A)  143 ft 
B)  121 ft 
C)  141 ft 
D)  142 ft 
E)  140 ft

Question 4

The __________ root of 125 is 5 because $5 ^ { 3 } = 125$

Accepted Answer

The answer of The __________ root of 125 is 5...

Question 5

A curved road will accommodate traffic traveling s mph if the radius of the curve is r feet, according to the formula $s = 3 \sqrt { r }$ . If engineers expect 55-mph traffic, what radius should they specify?
  
 Write your result to the nearest foot. $r$ =__________ ft

Accepted Answer

The answer of A curved road will accommodate traffic traveling...

Question 6

Solve $\sqrt [ 4 ] { x } = \sqrt { \frac { 3 x } { 7 } }$ . Write all proposed solutions. Cross out those that are extraneous solutions..

Accepted Answer

@#IMG-DLM& There are

Question 7

Multiply and simplify, if possible. $( 7 \sqrt [ 3 ] { 4 } ) ( 6 \sqrt [ 3 ] { 2 } )$

Accepted Answer

The answer of Multiply and simplify, if possible. \(( 7...

Question 8

Use rational exponents to simplfy the radical. All variables represent positive real numbers. $\sqrt [ 28 ] { x ^ { 7 } }$

Accepted Answer

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

Question 9

Simplify by combining like radicals. $\sqrt { 2 } + \sqrt { 72 }$

Accepted Answer

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

Question 10

Multiply and simplify, if possible. All variables represent positive real numbers. $2 \sqrt { 3 t } \left( 5 \sqrt { 3 t } + 2 \sqrt { 2 t ^ { 2 } } \right)$

Accepted Answer

A)  $30 \sqrt { t } + 4 t \sqrt { 6 t }$ 
B)  $30 \sqrt { t ^ { 2 } } + 4 t \sqrt { 6 t }$ 
C)  $30 t + 4 t ^ { 2 } \sqrt { 6 }$ 
D)  $30 t + 4 t \sqrt { 6 t }$ 
E)  $30 t + 4 \sqrt { 6 t ^ { 3 } }$ 
A)  $30 \sqrt { t } + 4 t \sqrt { 6 t }$ 
B)  $30 \sqrt { t ^ { 2 } } + 4 t \sqrt { 6 t }$ 
C)  $30 t + 4 t ^ { 2 } \sqrt { 6 }$ 
D)  $30 t + 4 t \sqrt { 6 t }$ 
E)  $30 t + 4 \sqrt { 6 t ^ { 3 } }$

Question 11

Simplify by combining like radicals. $2 \sqrt [ 3 ] { 320 } - \sqrt [ 3 ] { 135 } - 5 \sqrt [ 3 ] { 40 }$

Accepted Answer

The answer of Simplify by combining like radicals. \(2 \sqrt...

Question 12

Simplify the radical expression. The variable represents a positive real number. $\sqrt [ 3 ] { - 32 x ^ { 9 } }$

Accepted Answer

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

Question 13

Simplify the expression. All variables represent positive real numbers. $\left( 4 x ^ { 4 } \right) ^ { \frac { 3 } { 2 } }$

Accepted Answer

A)  $\left( 2 x ^ { 2 } \right) ^ { 3 }$ 
B)  $8 \left( x ^ { 4 } \right) ^ { \frac { 3 } { 2 } }$ 
C)  $8 x ^ { 6 }$ 
D)  $8 x ^ { 12 }$ 
E)  $8 x ^ { 2 }$ 
A)  $\left( 2 x ^ { 2 } \right) ^ { 3 }$ 
B)  $8 \left( x ^ { 4 } \right) ^ { \frac { 3 } { 2 } }$ 
C)  $8 x ^ { 6 }$ 
D)  $8 x ^ { 12 }$ 
E)  $8 x ^ { 2 }$

Question 14

Simplify the cube root. $\sqrt [ 3 ] { - 216 x ^ { 6 } }$

Accepted Answer

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

Question 15

Multiply and simplify, if possible. All variables represent positive real numbers. $( \sqrt { 7 x } + \sqrt { 2 y } ) ( \sqrt { 7 x } - \sqrt { 2 y } )$

Accepted Answer

The answer of Multiply and simplify, if possible. All variables...

Question 16

Perform the operation. Write the answer in a+bi   form. $( 7 + \sqrt { - 16 } ) + ( 6 + \sqrt { - 25 } )$

Accepted Answer

A)  $12 + 7 i$ 
B)  $11 + 6 i$ 
C)  $15 + 10 i$ 
D)  $13 + 9 i$ 
E)  $14 + 8 i$ 
A)  $12 + 7 i$ 
B)  $11 + 6 i$ 
C)  $15 + 10 i$ 
D)  $13 + 9 i$ 
E)  $14 + 8 i$

Question 17

Fill in the blank. $i ^ { 2 } =$$\underline{\quad\quad}$

Accepted Answer

The answer of Fill in the blank. \(i ^ {...

Question 18

Simplify the radical expression. All variables represent positive real numbers. $\sqrt { 75 a ^ { 2 } b ^ { 3 } }$

Accepted Answer

A)  $3 a b \sqrt { 5 b }$ 
B)  $5 a b \sqrt { 3 b }$ 
C)  $3 a b + \sqrt { 5 b }$ 
D)  $5 a b + \sqrt { 3 b }$ 
E)  $5 + a b \sqrt { 3 b }$ 
A)  $3 a b \sqrt { 5 b }$ 
B)  $5 a b \sqrt { 3 b }$ 
C)  $3 a b + \sqrt { 5 b }$ 
D)  $5 a b + \sqrt { 3 b }$ 
E)  $5 + a b \sqrt { 3 b }$

Question 19

Change the radical to an exponential expression. $\sqrt [ 6 ] { 4 a b c }$

Accepted Answer

The answer of Change the radical to an exponential expression....

Question 20

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

Accepted Answer

The answer of Simplify the expression. Write the answer without...

Find the distance between the pair of points. $( - 1 , - 1 ) , ( 7,5 )$

Rationalize the denominator. $\frac { \sqrt { 3 } + \sqrt { 2 } } { \sqrt { 3 } - \sqrt { 2 } }$

The lengths of two sides of the right triangle ABC are given. Find the length of the missing side. $b = 24$ ft and 145 ft

The __________ root of 125 is 5 because $5 ^ { 3 } = 125$

Solve $\sqrt [ 4 ] { x } = \sqrt { \frac { 3 x } { 7 } }$ . Write all proposed solutions. Cross out those that are extraneous solutions..

Multiply and simplify, if possible. $( 7 \sqrt [ 3 ] { 4 } ) ( 6 \sqrt [ 3 ] { 2 } )$

Use rational exponents to simplfy the radical. All variables represent positive real numbers. $\sqrt [ 28 ] { x ^ { 7 } }$

Simplify by combining like radicals. $\sqrt { 2 } + \sqrt { 72 }$

Multiply and simplify, if possible. All variables represent positive real numbers. $2 \sqrt { 3 t } \left( 5 \sqrt { 3 t } + 2 \sqrt { 2 t ^ { 2 } } \right)$

Simplify by combining like radicals. $2 \sqrt [ 3 ] { 320 } - \sqrt [ 3 ] { 135 } - 5 \sqrt [ 3 ] { 40 }$

Simplify the radical expression. The variable represents a positive real number. $\sqrt [ 3 ] { - 32 x ^ { 9 } }$

Simplify the expression. All variables represent positive real numbers. $\left( 4 x ^ { 4 } \right) ^ { \frac { 3 } { 2 } }$

Simplify the cube root. $\sqrt [ 3 ] { - 216 x ^ { 6 } }$

Multiply and simplify, if possible. All variables represent positive real numbers. $( \sqrt { 7 x } + \sqrt { 2 y } ) ( \sqrt { 7 x } - \sqrt { 2 y } )$

Perform the operation. Write the answer in a+bi form. $( 7 + \sqrt { - 16 } ) + ( 6 + \sqrt { - 25 } )$

Fill in the blank. $i ^ { 2 } =$ $\underline{\quad\quad}$

Simplify the radical expression. All variables represent positive real numbers. $\sqrt { 75 a ^ { 2 } b ^ { 3 } }$

Change the radical to an exponential expression. $\sqrt [ 6 ] { 4 a b c }$

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

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

Find the distance between the pair of points. (−1,−1),(7,5)( - 1 , - 1 ) , ( 7,5 )(−1,−1),(7,5)

Rationalize the denominator. 3+23−2\frac { \sqrt { 3 } + \sqrt { 2 } } { \sqrt { 3 } - \sqrt { 2 } }3​−2​3​+2​​

The lengths of two sides of the right triangle ABC are given. Find the length of the missing side. b=24b = 24b=24 ft and 145 ft

The __________ root of 125 is 5 because 53=1255 ^ { 3 } = 12553=125

A curved road will accommodate traffic traveling s mph if the radius of the curve is r feet, according to the formula s=3rs = 3 \sqrt { r }s=3r​ . If engineers expect 55-mph traffic, what radius should they specify? Write your result to the nearest foot. rrr =__________ ft

Solve x4=3x7\sqrt [ 4 ] { x } = \sqrt { \frac { 3 x } { 7 } }4x​=73x​​ . Write all proposed solutions. Cross out those that are extraneous solutions..

Multiply and simplify, if possible. (743)(623)( 7 \sqrt [ 3 ] { 4 } ) ( 6 \sqrt [ 3 ] { 2 } )(734​)(632​)

Use rational exponents to simplfy the radical. All variables represent positive real numbers. x728\sqrt [ 28 ] { x ^ { 7 } }28x7​

Simplify by combining like radicals. 2+72\sqrt { 2 } + \sqrt { 72 }2​+72​

Multiply and simplify, if possible. All variables represent positive real numbers. 23t(53t+22t2)2 \sqrt { 3 t } \left( 5 \sqrt { 3 t } + 2 \sqrt { 2 t ^ { 2 } } \right)23t​(53t​+22t2​)

Simplify by combining like radicals. 23203−1353−54032 \sqrt [ 3 ] { 320 } - \sqrt [ 3 ] { 135 } - 5 \sqrt [ 3 ] { 40 }23320​−3135​−5340​

Simplify the radical expression. The variable represents a positive real number. −32x93\sqrt [ 3 ] { - 32 x ^ { 9 } }3−32x9​

Simplify the expression. All variables represent positive real numbers. (4x4)32\left( 4 x ^ { 4 } \right) ^ { \frac { 3 } { 2 } }(4x4)23​

Simplify the cube root. −216x63\sqrt [ 3 ] { - 216 x ^ { 6 } }3−216x6​

Multiply and simplify, if possible. All variables represent positive real numbers. (7x+2y)(7x−2y)( \sqrt { 7 x } + \sqrt { 2 y } ) ( \sqrt { 7 x } - \sqrt { 2 y } )(7x​+2y​)(7x​−2y​)

Perform the operation. Write the answer in a+bi form. (7+−16)+(6+−25)( 7 + \sqrt { - 16 } ) + ( 6 + \sqrt { - 25 } )(7+−16​)+(6+−25​)

Fill in the blank. i2=i ^ { 2 } =i2=‾\underline{\quad\quad}​

Simplify the radical expression. All variables represent positive real numbers. 75a2b3\sqrt { 75 a ^ { 2 } b ^ { 3 } }75a2b3​

Change the radical to an exponential expression. 4abc6\sqrt [ 6 ] { 4 a b c }64abc​

Simplify the expression. Write the answer without negative exponents. 5−135−535 ^ { - \frac { 1 } { 3 } } 5 ^ { - \frac { 5 } { 3 } }5−31​5−35​

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

Find the distance between the pair of points. $( - 1 , - 1 ) , ( 7,5 )$

Rationalize the denominator. $\frac { \sqrt { 3 } + \sqrt { 2 } } { \sqrt { 3 } - \sqrt { 2 } }$

The lengths of two sides of the right triangle ABC are given. Find the length of the missing side. $b = 24$ ft and 145 ft

The __________ root of 125 is 5 because $5 ^ { 3 } = 125$

Solve $\sqrt [ 4 ] { x } = \sqrt { \frac { 3 x } { 7 } }$ . Write all proposed solutions. Cross out those that are extraneous solutions..

Multiply and simplify, if possible. $( 7 \sqrt [ 3 ] { 4 } ) ( 6 \sqrt [ 3 ] { 2 } )$

Use rational exponents to simplfy the radical. All variables represent positive real numbers. $\sqrt [ 28 ] { x ^ { 7 } }$

Simplify by combining like radicals. $\sqrt { 2 } + \sqrt { 72 }$

Multiply and simplify, if possible. All variables represent positive real numbers. $2 \sqrt { 3 t } \left( 5 \sqrt { 3 t } + 2 \sqrt { 2 t ^ { 2 } } \right)$

Simplify by combining like radicals. $2 \sqrt [ 3 ] { 320 } - \sqrt [ 3 ] { 135 } - 5 \sqrt [ 3 ] { 40 }$

Simplify the radical expression. The variable represents a positive real number. $\sqrt [ 3 ] { - 32 x ^ { 9 } }$

Simplify the expression. All variables represent positive real numbers. $\left( 4 x ^ { 4 } \right) ^ { \frac { 3 } { 2 } }$

Simplify the cube root. $\sqrt [ 3 ] { - 216 x ^ { 6 } }$

Multiply and simplify, if possible. All variables represent positive real numbers. $( \sqrt { 7 x } + \sqrt { 2 y } ) ( \sqrt { 7 x } - \sqrt { 2 y } )$

Perform the operation. Write the answer in a+bi form. $( 7 + \sqrt { - 16 } ) + ( 6 + \sqrt { - 25 } )$

Fill in the blank. $i ^ { 2 } =$ $\underline{\quad\quad}$

Simplify the radical expression. All variables represent positive real numbers. $\sqrt { 75 a ^ { 2 } b ^ { 3 } }$

Change the radical to an exponential expression. $\sqrt [ 6 ] { 4 a b c }$

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