Question 1

Simplify the radical expression. $\frac { 11 \sqrt { 98 } } { 63 }$

Accepted Answer

A)  $\frac { 11 \sqrt { 2 } } { 9 }$ 
B)  $\frac { 11 \sqrt { 7 } } { 18 }$ 
C)  $\frac { 11 \sqrt { 2 } } { 18 }$ 
D)  $\frac { 22 \sqrt { 7 } } { 63 }$ 
A)  $\frac { 11 \sqrt { 2 } } { 9 }$ 
B)  $\frac { 11 \sqrt { 7 } } { 18 }$ 
C)  $\frac { 11 \sqrt { 2 } } { 18 }$ 
D)  $\frac { 22 \sqrt { 7 } } { 63 }$

Question 2

Add or subtract the radical expressions as indicated. Assume that all variables represent positive real numbers. $$3 \sqrt { 3 y } - \sqrt { 27 y ^ { 5 } } + y ^ { 2 } \sqrt { 75 y }$$

Accepted Answer

The answer of Add or subtract the radical expressions as...

Question 3

Add or subtract the radical expressions as indicated, if possible. $9 \sqrt { 2 } + \sqrt { 162 } - 3 \sqrt { 18 }$

Accepted Answer

A)  $54 \sqrt { 2 }$ 
B)  $63 \sqrt { 2 }$ 
C)  $9 \sqrt { 2 }$ 
D)  $6 \sqrt { 146 }$ 
A)  $54 \sqrt { 2 }$ 
B)  $63 \sqrt { 2 }$ 
C)  $9 \sqrt { 2 }$ 
D)  $6 \sqrt { 146 }$

Question 4

Evaluate the root without using a calculator or note that root is not a real number. $\sqrt { \frac { 49 } { 121 } }$

Accepted Answer

A)  $- \frac { 7 } { 11 }$ 
B)  $\frac { 7 } { 121 }$ 
C)  $\frac { 7 } { 11 }$ 
D)  Not a real number 
A)  $- \frac { 7 } { 11 }$ 
B)  $\frac { 7 } { 121 }$ 
C)  $\frac { 7 } { 11 }$ 
D)  Not a real number

Question 5

Add or subtract the radical expressions as indicated, if possible. 
$7 \sqrt { 2 } + \sqrt { 98 }$

Accepted Answer

A)  28 
B)  70 
C)  $14 \sqrt { 2 }$ 
D)  Cannot be simplified further 
A)  28 
B)  70 
C)  $14 \sqrt { 2 }$ 
D)  Cannot be simplified further

Question 6

Rationalize the denominator. $$\frac { x } { y - \sqrt { 6 } }$$

Accepted Answer

A)  $\frac { x y + x \sqrt { 6 } } { y ^ { 2 } - 6 }$ 
B)  $\frac { x y - x \sqrt { 6 } } { y ^ { 2 } - 36 }$ 
C)  $\frac { x y - x \sqrt { 6 } } { y ^ { 2 } - 6 }$ 
D)  $\frac { x \sqrt { 6 } } { y - 6 }$ 
A)  $\frac { x y + x \sqrt { 6 } } { y ^ { 2 } - 6 }$ 
B)  $\frac { x y - x \sqrt { 6 } } { y ^ { 2 } - 36 }$ 
C)  $\frac { x y - x \sqrt { 6 } } { y ^ { 2 } - 6 }$ 
D)  $\frac { x \sqrt { 6 } } { y - 6 }$

Question 7

Solve the equation. $$9 = 13 + ( q - 3 ) ^ { 1 / 3 }$$

Accepted Answer

A)  {61} 
B)  {-61} 
C)  {67} 
D)  { } 
A)  {61} 
B)  {-61} 
C)  {67} 
D)  { }

Question 8

Use the Pythagorean theorem to find b when a = h and c = 5.

Accepted Answer

A)  $b = \sqrt { 5 - h }$ 
B)  $b = 25 - h ^ { 2 }$ 
C)  $b = \sqrt { 25 - h ^ { 2 } }$ 
D)  $b = 5 - h$ 
A)  $b = \sqrt { 5 - h }$ 
B)  $b = 25 - h ^ { 2 }$ 
C)  $b = \sqrt { 25 - h ^ { 2 } }$ 
D)  $b = 5 - h$

Question 9

The amount of time it takes an object dropped from an initial height of h0 feet to reach a height of h feet is given by the formula $t = \sqrt { \frac { h _ { 0 } - h } { 16 } }$ An object dropped from the top of the Sears Tower in Chicago takes 9.5 seconds to reach the ground. Use the Above equation to approximate the height of the Sears Tower.

Accepted Answer

A)  1,520 feet 
B)  1,170 feet 
C)  1,444 feet 
D)  990 feet 
A)  1,520 feet 
B)  1,170 feet 
C)  1,444 feet 
D)  990 feet

Question 10

Simplify the expression. Assume all variables represent positive real numbers. $$( \sqrt [ 6 ] { 3 x y } ) ^ { 6 }$$

Accepted Answer

A)  $\sqrt { 3 x y }$ 
B)  $3 x y$ 
C)  $\sqrt [ 6 ] { 3 } x y$ 
D)  $3 \sqrt [ 6 ] { x y }$ 
A)  $\sqrt { 3 x y }$ 
B)  $3 x y$ 
C)  $\sqrt [ 6 ] { 3 } x y$ 
D)  $3 \sqrt [ 6 ] { x y }$

Question 11

Multiply the radical expressions and simplify your answer. 
$- 2 \sqrt { 6 x ^ { 8 } y ^ { 3 } } \cdot 4 \sqrt { 10 x y ^ { 8 } }$

Accepted Answer

A)  $- 32 x ^ { 4 } y ^ { 5 } \sqrt { 15 x y }$ 
B)  $- 32 \sqrt { x ^ { 7 } y ^ { 9 } }$ 
C)  $- 16 \sqrt { 15 x ^ { 9 } y ^ { 11 } }$ 
D)  $- 16 x ^ { 4 } y ^ { 5 } \sqrt { 15 x y }$ 
A)  $- 32 x ^ { 4 } y ^ { 5 } \sqrt { 15 x y }$ 
B)  $- 32 \sqrt { x ^ { 7 } y ^ { 9 } }$ 
C)  $- 16 \sqrt { 15 x ^ { 9 } y ^ { 11 } }$ 
D)  $- 16 x ^ { 4 } y ^ { 5 } \sqrt { 15 x y }$

Question 12

Simplify the expression. $( - 121 ) ^ { 5 / 2 }$

Accepted Answer

A)  $- \frac { 605 } { 2 }$ 
B)  161,051 
C)  $- 161,051$ 
D)  Not a real number 
A)  $- \frac { 605 } { 2 }$ 
B)  161,051 
C)  $- 161,051$ 
D)  Not a real number

Question 13

Write the expression by using rational exponents rather than radical notation. $$\sqrt [ 3 ] { 18 t }$$

Accepted Answer

The answer of Write the expression by using rational exponents...

Question 14

Subtract the radical expressions, if possible. $$2 \sqrt [ 3 ] { 14 } - 14 \sqrt [ 3 ] { 14 }$$

Accepted Answer

A)  $- 12$ 
B)  $16 \sqrt [ 3 ] { 14 }$ 
C)  $- 12 \sqrt [ 3 ] { 14 }$ 
D)  Cannot be simplified further 
A)  $- 12$ 
B)  $16 \sqrt [ 3 ] { 14 }$ 
C)  $- 12 \sqrt [ 3 ] { 14 }$ 
D)  Cannot be simplified further

Question 15

Evaluate the root without using a calculator or note that root is not a real number. $\sqrt [ 4 ] { 16 }$

Accepted Answer

A)  2 
B)  $- 2$ 
C)  3 
D)  Not a real number 
A)  2 
B)  $- 2$ 
C)  3 
D)  Not a real number

Question 16

Add or subtract the radical expressions as indicated, if possible. $5 \sqrt { 3 a } - \sqrt { 27 a } - \sqrt { 48 a }$

Accepted Answer

A)  $- 2 \sqrt { 3 a }$ 
B)  $5 \sqrt { 3 a } - 7 \sqrt { a }$ 
C)  $- 20 \sqrt { 3 a }$ 
D)  Cannot be simplified further 
A)  $- 2 \sqrt { 3 a }$ 
B)  $5 \sqrt { 3 a } - 7 \sqrt { a }$ 
C)  $- 20 \sqrt { 3 a }$ 
D)  Cannot be simplified further

Question 17

Rationalize the denominator and simplify completely. $$\frac { 11 } { \sqrt [ 3 ] { 36 } }$$

Accepted Answer

A)  66 
B)  11 
C)  $\frac { 11 \sqrt [ 3 ] { 6 } } { 6 }$ 
D)  $11 \sqrt [ 3 ] { 6 }$ 
A)  66 
B)  11 
C)  $\frac { 11 \sqrt [ 3 ] { 6 } } { 6 }$ 
D)  $11 \sqrt [ 3 ] { 6 }$

Question 18

Simplify the radical expression. $$\sqrt [ 3 ] { ( - 5 ) ^ { 3 } }$$

Accepted Answer

A)  -5 
B)  5 
C)  -125 
D)  125 
A)  -5 
B)  5 
C)  -125 
D)  125

Question 19

Rationalize the denominator. $$\frac { \sqrt { a } + \sqrt { b } } { \sqrt { c } - \sqrt { d } }$$

Accepted Answer

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

Question 20

Subtract. Write the answer in the form a + bi. $$( - 4 + 7 i ) - ( 11 - 19 i )$$

Accepted Answer

A)  $- 41$ 
B)  $3 - 30 i$ 
C)  $- 15 + 26 i$ 
D)  $- 15 - 12 i$ 
A)  $- 41$ 
B)  $3 - 30 i$ 
C)  $- 15 + 26 i$ 
D)  $- 15 - 12 i$

Simplify the radical expression. $\frac { 11 \sqrt { 98 } } { 63 }$

Add or subtract the radical expressions as indicated. Assume that all variables represent positive real numbers. $3 \sqrt { 3 y } - \sqrt { 27 y ^ { 5 } } + y ^ { 2 } \sqrt { 75 y }$

Add or subtract the radical expressions as indicated, if possible. $9 \sqrt { 2 } + \sqrt { 162 } - 3 \sqrt { 18 }$

Evaluate the root without using a calculator or note that root is not a real number. $\sqrt { \frac { 49 } { 121 } }$

Add or subtract the radical expressions as indicated, if possible. $7 \sqrt { 2 } + \sqrt { 98 }$

Rationalize the denominator. $\frac { x } { y - \sqrt { 6 } }$

Solve the equation. $9 = 13 + ( q - 3 ) ^ { 1 / 3 }$

Use the Pythagorean theorem to find b when a = h and c = 5.

Simplify the expression. Assume all variables represent positive real numbers. $( \sqrt [ 6 ] { 3 x y } ) ^ { 6 }$

Multiply the radical expressions and simplify your answer. $- 2 \sqrt { 6 x ^ { 8 } y ^ { 3 } } \cdot 4 \sqrt { 10 x y ^ { 8 } }$

Simplify the expression. $( - 121 ) ^ { 5 / 2 }$

Write the expression by using rational exponents rather than radical notation. $\sqrt [ 3 ] { 18 t }$

Subtract the radical expressions, if possible. $2 \sqrt [ 3 ] { 14 } - 14 \sqrt [ 3 ] { 14 }$

Evaluate the root without using a calculator or note that root is not a real number. $\sqrt [ 4 ] { 16 }$

Add or subtract the radical expressions as indicated, if possible. $5 \sqrt { 3 a } - \sqrt { 27 a } - \sqrt { 48 a }$

Rationalize the denominator and simplify completely. $\frac { 11 } { \sqrt [ 3 ] { 36 } }$

Simplify the radical expression. $\sqrt [ 3 ] { ( - 5 ) ^ { 3 } }$

Rationalize the denominator. $\frac { \sqrt { a } + \sqrt { b } } { \sqrt { c } - \sqrt { d } }$

Subtract. Write the answer in the form a + bi. $( - 4 + 7 i ) - ( 11 - 19 i )$

Linear Equations and Inequalities in One Variable

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Exam 6: Radicals and Complex Numbers

Simplify the radical expression. 119863\frac { 11 \sqrt { 98 } } { 63 }631198​​

Add or subtract the radical expressions as indicated. Assume that all variables represent positive real numbers. 33y−27y5+y275y3 \sqrt { 3 y } - \sqrt { 27 y ^ { 5 } } + y ^ { 2 } \sqrt { 75 y }33y​−27y5​+y275y​

Add or subtract the radical expressions as indicated, if possible. 92+162−3189 \sqrt { 2 } + \sqrt { 162 } - 3 \sqrt { 18 }92​+162​−318​

Evaluate the root without using a calculator or note that root is not a real number. 49121\sqrt { \frac { 49 } { 121 } }12149​​

Add or subtract the radical expressions as indicated, if possible. 72+987 \sqrt { 2 } + \sqrt { 98 }72​+98​

Rationalize the denominator. xy−6\frac { x } { y - \sqrt { 6 } }y−6​x​

Solve the equation. 9=13+(q−3)1/39 = 13 + ( q - 3 ) ^ { 1 / 3 }9=13+(q−3)1/3

Use the Pythagorean theorem to find b when a = h and c = 5.

Simplify the expression. Assume all variables represent positive real numbers. (3xy6)6( \sqrt [ 6 ] { 3 x y } ) ^ { 6 }(63xy​)6

Multiply the radical expressions and simplify your answer. −26x8y3⋅410xy8- 2 \sqrt { 6 x ^ { 8 } y ^ { 3 } } \cdot 4 \sqrt { 10 x y ^ { 8 } }−26x8y3​⋅410xy8​

Simplify the expression. (−121)5/2( - 121 ) ^ { 5 / 2 }(−121)5/2

Write the expression by using rational exponents rather than radical notation. 18t3\sqrt [ 3 ] { 18 t }318t​

Subtract the radical expressions, if possible. 2143−141432 \sqrt [ 3 ] { 14 } - 14 \sqrt [ 3 ] { 14 }2314​−14314​

Evaluate the root without using a calculator or note that root is not a real number. 164\sqrt [ 4 ] { 16 }416​

Add or subtract the radical expressions as indicated, if possible. 53a−27a−48a5 \sqrt { 3 a } - \sqrt { 27 a } - \sqrt { 48 a }53a​−27a​−48a​

Rationalize the denominator and simplify completely. 11363\frac { 11 } { \sqrt [ 3 ] { 36 } }336​11​

Simplify the radical expression. (−5)33\sqrt [ 3 ] { ( - 5 ) ^ { 3 } }3(−5)3​

Rationalize the denominator. a+bc−d\frac { \sqrt { a } + \sqrt { b } } { \sqrt { c } - \sqrt { d } }c​−d​a​+b​​

Subtract. Write the answer in the form a + bi. (−4+7i)−(11−19i)( - 4 + 7 i ) - ( 11 - 19 i )(−4+7i)−(11−19i)

Linear Equations and Inequalities in One Variable

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Simplify the radical expression. $\frac { 11 \sqrt { 98 } } { 63 }$

Add or subtract the radical expressions as indicated. Assume that all variables represent positive real numbers. $3 \sqrt { 3 y } - \sqrt { 27 y ^ { 5 } } + y ^ { 2 } \sqrt { 75 y }$

Add or subtract the radical expressions as indicated, if possible. $9 \sqrt { 2 } + \sqrt { 162 } - 3 \sqrt { 18 }$

Evaluate the root without using a calculator or note that root is not a real number. $\sqrt { \frac { 49 } { 121 } }$

Add or subtract the radical expressions as indicated, if possible. $7 \sqrt { 2 } + \sqrt { 98 }$

Rationalize the denominator. $\frac { x } { y - \sqrt { 6 } }$

Solve the equation. $9 = 13 + ( q - 3 ) ^ { 1 / 3 }$

Simplify the expression. Assume all variables represent positive real numbers. $( \sqrt [ 6 ] { 3 x y } ) ^ { 6 }$

Multiply the radical expressions and simplify your answer. $- 2 \sqrt { 6 x ^ { 8 } y ^ { 3 } } \cdot 4 \sqrt { 10 x y ^ { 8 } }$

Simplify the expression. $( - 121 ) ^ { 5 / 2 }$

Write the expression by using rational exponents rather than radical notation. $\sqrt [ 3 ] { 18 t }$

Subtract the radical expressions, if possible. $2 \sqrt [ 3 ] { 14 } - 14 \sqrt [ 3 ] { 14 }$

Evaluate the root without using a calculator or note that root is not a real number. $\sqrt [ 4 ] { 16 }$

Add or subtract the radical expressions as indicated, if possible. $5 \sqrt { 3 a } - \sqrt { 27 a } - \sqrt { 48 a }$

Rationalize the denominator and simplify completely. $\frac { 11 } { \sqrt [ 3 ] { 36 } }$

Simplify the radical expression. $\sqrt [ 3 ] { ( - 5 ) ^ { 3 } }$

Rationalize the denominator. $\frac { \sqrt { a } + \sqrt { b } } { \sqrt { c } - \sqrt { d } }$

Subtract. Write the answer in the form a + bi. $( - 4 + 7 i ) - ( 11 - 19 i )$