Question 1

Perform the indicated operation. Write the result in the form a + bi.
-$$( 8 - 7 i ) + ( - 8 + 7 i )$$

Accepted Answer

A)  $- 16 + 14 i$ 
B)  $16 - 14 \mathrm { i }$ 
C)  0 
D)  $- 16 - 14 i$ 
A)  $- 16 + 14 i$ 
B)  $16 - 14 \mathrm { i }$ 
C)  0 
D)  $- 16 - 14 i$

Question 2

Add or subtract. Assume all variables represent positive real numbers.
-$$- \frac { \sqrt [ 3 ] { 2 x ^ { 4 } } } { 25 } + \sqrt [ 3 ] { \frac { 128 x ^ { 4 } } { 125 } }$$

Accepted Answer

A)  $\frac { 19 x ^ { 2 } \sqrt [ 3 ] { 2 } } { 25 }$ 
B)  $\frac { 19 x \sqrt [ 3 ] { 2 x } } { 25 }$ 
C)  $\frac { 20 x \sqrt [ 3 ] { 3 x } } { 25 }$ 
D)  $- \frac { 19 x \sqrt [ 3 ] { 2 x } } { 5 }$ 
A)  $\frac { 19 x ^ { 2 } \sqrt [ 3 ] { 2 } } { 25 }$ 
B)  $\frac { 19 x \sqrt [ 3 ] { 2 x } } { 25 }$ 
C)  $\frac { 20 x \sqrt [ 3 ] { 3 x } } { 25 }$ 
D)  $- \frac { 19 x \sqrt [ 3 ] { 2 x } } { 5 }$

Question 3

Find the square root. Assume that all variables represent nonnegative real numbers.
-$$\sqrt { 49 x ^ { 12 } }$$

Accepted Answer

A)  $49 x ^ { 6 }$ 
B)  $7 x ^ { 6 }$ 
C)  $7 x ^ { 12 }$ 
D)  $7 x ^ { 2 }$ 
A)  $49 x ^ { 6 }$ 
B)  $7 x ^ { 6 }$ 
C)  $7 x ^ { 12 }$ 
D)  $7 x ^ { 2 }$

Question 4

Solve.
-$$\sqrt { x } + 1 = \sqrt { x + 11 }$$

Accepted Answer

A)  $x = 25$ 
B)  $x = 100$ 
C)  $x = 5$ 
D)  $\varnothing$ 
A)  $x = 25$ 
B)  $x = 100$ 
C)  $x = 5$ 
D)  $\varnothing$

Question 5

Raise to the power or find the root. Assume that all variables represent positive real numbers. Write with only positive
exponents.
-$3 x ^ { - 1 / 5 } \left( 2 x ^ { 4 } - x ^ { 1 / 5 } \right)$

Accepted Answer

A)  $6 x ^ { 19 / 5 } - 1$ 
B)  $6 x ^ { 19 / 5 } - 3$ 
C)  $6 x ^ { 19 / 5 } - x$ 
D)  $6 x ^ { 19 / 5 } - 3 x$ 
A)  $6 x ^ { 19 / 5 } - 1$ 
B)  $6 x ^ { 19 / 5 } - 3$ 
C)  $6 x ^ { 19 / 5 } - x$ 
D)  $6 x ^ { 19 / 5 } - 3 x$

Question 6

Simplify. Assume that all variables represent any real number.
-$$\sqrt { ( - 8 ) ^ { 2 } }$$

Accepted Answer

A)  $- 64$ 
B)  8 
C)  $- 8$ 
D)  64 
A)  $- 64$ 
B)  8 
C)  $- 8$ 
D)  64

Question 7

Use a calculator to approximate the square root to 3 decimal places. Check to see that the approximation is reasonable.
-$\sqrt { 78 }$

Accepted Answer

A)  $8.837$ 
B)  $78.000$ 
C)  $8.832$ 
D)  $8.829$ 
A)  $8.837$ 
B)  $78.000$ 
C)  $8.832$ 
D)  $8.829$

Question 8

Raise to the power or find the root. Assume that all variables represent positive real numbers. Write with only positive
exponents.
-$- \sqrt [ 5 ] { x ^ { 15 } }$

Accepted Answer

A)  $- x ^ { 3 }$ 
B)  $- x ^ { 5 }$ 
C)  $- 3 x$ 
D)  $- x ^ { 4 }$ 
A)  $- x ^ { 3 }$ 
B)  $- x ^ { 5 }$ 
C)  $- 3 x$ 
D)  $- x ^ { 4 }$

Question 9

Fill in the blank with one of the words or phrases listed below.

-The , written i, is the number whose square is -1.

Accepted Answer

A) imaginary unit 
B)  index 
C)  conjugate 
D)  complex number 
A) imaginary unit 
B)  index 
C)  conjugate 
D)  complex number

Question 10

Simplify. Assume that all variables represent positive real numbers.
-$\sqrt { 72 x ^ { 2 } }$

Accepted Answer

A)  $6 \sqrt { 2 x }$ 
B)  $2 x ^ { 2 } \sqrt { 6 }$ 
C)  $6 \times \sqrt { 2 }$ 
D)  $72 \mathrm { x }$ 
A)  $6 \sqrt { 2 x }$ 
B)  $2 x ^ { 2 } \sqrt { 6 }$ 
C)  $6 \times \sqrt { 2 }$ 
D)  $72 \mathrm { x }$

Question 11

Find the midpoint of the line segment whose endpoints are given.
-$$( - 4.5 , - 1.8 ) , ( - 7.5,7.6 )$$

Accepted Answer

A)  $( - 6 , - 2.9 )$ 
B)  $( 6,2.9 )$ 
C)  $( - 6,2.9 )$ 
D)  $( 1.5 , - 4.7 )$ 
A)  $( - 6 , - 2.9 )$ 
B)  $( 6,2.9 )$ 
C)  $( - 6,2.9 )$ 
D)  $( 1.5 , - 4.7 )$

Question 12

Find the cube root.
-$\sqrt [ 3 ] { 729 }$

Accepted Answer

A)  81 
B)  9 
C)  27 
D)  not a real number 
A)  81 
B)  9 
C)  27 
D)  not a real number

Question 13

Find all real square roots of the number.
36

Accepted Answer

A)   12, -12 
B)   7, -7 
C)   8, -8 
D)   6, -6 
A)   12, -12 
B)   7, -7 
C)   8, -8 
D)   6, -6

Question 14

Rationalize the numerator and simplify. Assume all variables represent positive real numbers.
-$$\frac { 1 - \sqrt { 6 } } { 1 + \sqrt { 6 } }$$

Accepted Answer

A)  $\frac { 7 } { - 5 - 2 \sqrt { 6 } }$ 
B)  $\frac { - 5 } { 7 - 2 \sqrt { 6 } }$ 
C)  $\frac { - 5 } { 7 + 2 \sqrt { 6 } }$ 
D)  1 
A)  $\frac { 7 } { - 5 - 2 \sqrt { 6 } }$ 
B)  $\frac { - 5 } { 7 - 2 \sqrt { 6 } }$ 
C)  $\frac { - 5 } { 7 + 2 \sqrt { 6 } }$ 
D)  1

Question 15

Write in terms of i.
-$\sqrt { - 4 }$

Accepted Answer

A)  $\pm 2$ 
B)  $- 2 \mathrm { i }$ 
C)  $2 \mathrm { i }$ 
D)  $- \mathrm { i } \sqrt { 2 }$ 
A)  $\pm 2$ 
B)  $- 2 \mathrm { i }$ 
C)  $2 \mathrm { i }$ 
D)  $- \mathrm { i } \sqrt { 2 }$

Question 16

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers.
-$\sqrt { \frac { 36 } { x } }$

Accepted Answer

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

Question 17

Simplify. Assume that all variables represent any real number.
-$$\sqrt { ( x + 8 ) ^ { 2 } }$$

Accepted Answer

A)  $x + 8$ 
B)  $- | x + 8 |$ 
C)  $| x + 8 |$ 
D)  $- x - 8$ 
A)  $x + 8$ 
B)  $- | x + 8 |$ 
C)  $| x + 8 |$ 
D)  $- x - 8$

Question 18

Solve.
-$$\sqrt { 11 x - 9 } = \sqrt { 9 - 11 x }$$

Accepted Answer

A)  $\frac { 11 } { 9 }$ 
B)  $- \frac { 9 } { 11 }$ 
C)  $\frac { 9 } { 11 }$ 
D)  $\varnothing$ 
A)  $\frac { 11 } { 9 }$ 
B)  $- \frac { 9 } { 11 }$ 
C)  $\frac { 9 } { 11 }$ 
D)  $\varnothing$

Question 19

Perform the indicated operation. Write the result in the form a + bi.
-(14i)(-2i)

Accepted Answer

A)  $- 28 \mathrm { i }$ 
B)  28 
C)  $28 \mathrm { i }$ 
D)  $- 28$ 
A)  $- 28 \mathrm { i }$ 
B)  28 
C)  $28 \mathrm { i }$ 
D)  $- 28$

Question 20

Perform the indicated operation and simplify. Write the result in the form a + bi.
-$$( 4 + 10 \mathrm { i } ) ^ { 2 }$$

Accepted Answer

A)  $16 + 100 \mathrm { i }$ 
B)  $- 84 + 80 \mathrm { i }$ 
C)  $116 + 80 \mathrm { i }$ 
D)  $16 - 100 \mathrm { i }$ 
A)  $16 + 100 \mathrm { i }$ 
B)  $- 84 + 80 \mathrm { i }$ 
C)  $116 + 80 \mathrm { i }$ 
D)  $16 - 100 \mathrm { i }$

Perform the indicated operation. Write the result in the form a + bi. - $( 8 - 7 i ) + ( - 8 + 7 i )$

Add or subtract. Assume all variables represent positive real numbers. - $- \frac { \sqrt [ 3 ] { 2 x ^ { 4 } } } { 25 } + \sqrt [ 3 ] { \frac { 128 x ^ { 4 } } { 125 } }$

Find the square root. Assume that all variables represent nonnegative real numbers. - $\sqrt { 49 x ^ { 12 } }$

Solve. - $\sqrt { x } + 1 = \sqrt { x + 11 }$

Raise to the power or find the root. Assume that all variables represent positive real numbers. Write with only positive exponents. - $3 x ^ { - 1 / 5 } \left( 2 x ^ { 4 } - x ^ { 1 / 5 } \right)$

Simplify. Assume that all variables represent any real number. - $\sqrt { ( - 8 ) ^ { 2 } }$

Use a calculator to approximate the square root to 3 decimal places. Check to see that the approximation is reasonable. - $\sqrt { 78 }$

Raise to the power or find the root. Assume that all variables represent positive real numbers. Write with only positive exponents. - $- \sqrt [ 5 ] { x ^ { 15 } }$

Fill in the blank with one of the words or phrases listed below. -The , written i, is the number whose square is -1.

Simplify. Assume that all variables represent positive real numbers. - $\sqrt { 72 x ^ { 2 } }$

Find the midpoint of the line segment whose endpoints are given. - $( - 4.5 , - 1.8 ) , ( - 7.5,7.6 )$

Find the cube root. - $\sqrt [ 3 ] { 729 }$

Find all real square roots of the number. 36

Rationalize the numerator and simplify. Assume all variables represent positive real numbers. - $\frac { 1 - \sqrt { 6 } } { 1 + \sqrt { 6 } }$

Write in terms of i. - $\sqrt { - 4 }$

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers. - $\sqrt { \frac { 36 } { x } }$

Simplify. Assume that all variables represent any real number. - $\sqrt { ( x + 8 ) ^ { 2 } }$

Solve. - $\sqrt { 11 x - 9 } = \sqrt { 9 - 11 x }$

Perform the indicated operation. Write the result in the form a + bi. -(14i)(-2i)

Perform the indicated operation and simplify. Write the result in the form a + bi. - $( 4 + 10 \mathrm { i } ) ^ { 2 }$

Real Numbers and Algebraic Expressions

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Exam 7: Rational Exponents, Radicals, and Complex Numbers

Perform the indicated operation. Write the result in the form a + bi. - (8−7i)+(−8+7i)( 8 - 7 i ) + ( - 8 + 7 i )(8−7i)+(−8+7i)

Add or subtract. Assume all variables represent positive real numbers. - −2x4325+128x41253- \frac { \sqrt [ 3 ] { 2 x ^ { 4 } } } { 25 } + \sqrt [ 3 ] { \frac { 128 x ^ { 4 } } { 125 } }−2532x4​​+3125128x4​​

Find the square root. Assume that all variables represent nonnegative real numbers. - 49x12\sqrt { 49 x ^ { 12 } }49x12​

Solve. - x+1=x+11\sqrt { x } + 1 = \sqrt { x + 11 }x​+1=x+11​

Raise to the power or find the root. Assume that all variables represent positive real numbers. Write with only positive exponents. - 3x−1/5(2x4−x1/5)3 x ^ { - 1 / 5 } \left( 2 x ^ { 4 } - x ^ { 1 / 5 } \right)3x−1/5(2x4−x1/5)

Simplify. Assume that all variables represent any real number. - (−8)2\sqrt { ( - 8 ) ^ { 2 } }(−8)2​

Use a calculator to approximate the square root to 3 decimal places. Check to see that the approximation is reasonable. - 78\sqrt { 78 }78​

Raise to the power or find the root. Assume that all variables represent positive real numbers. Write with only positive exponents. - −x155- \sqrt [ 5 ] { x ^ { 15 } }−5x15​