Question 1

Write in terms of i.
-$\sqrt { - 400 }$

Accepted Answer

A)  $- 20 \mathrm { i }$ 
B)  $20 \mathrm { i }$ 
C)  $\mathrm { i } \sqrt { 20 }$ 
D)  $\pm 20$ 
A)  $- 20 \mathrm { i }$ 
B)  $20 \mathrm { i }$ 
C)  $\mathrm { i } \sqrt { 20 }$ 
D)  $\pm 20$

Question 2

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers.
-$\frac { 8 } { \sqrt [ 3 ] { y } }$

Accepted Answer

A)  $\frac { 8 \sqrt [ 3 ] { y ^ { 2 } } } { y }$ 
B)  $8 y$ 
C)  $\frac { 8 \sqrt [ 3 ] { y } } { y }$ 
D)  $8 \sqrt [ 3 ] { y ^ { 2 } }$ 
A)  $\frac { 8 \sqrt [ 3 ] { y ^ { 2 } } } { y }$ 
B)  $8 y$ 
C)  $\frac { 8 \sqrt [ 3 ] { y } } { y }$ 
D)  $8 \sqrt [ 3 ] { y ^ { 2 } }$

Question 3

Use the Pythagorean theorem to find the unknown side of the right triangle.
-

Accepted Answer

A)  $7 \sqrt { 6 }$ 
B)  91 
C)  $7 \sqrt { 13 }$ 
D)  35 
A)  $7 \sqrt { 6 }$ 
B)  91 
C)  $7 \sqrt { 13 }$ 
D)  35

Question 4

Raise to the power or find the root. Assume that all variables represent positive real numbers. Write with only positive
exponents.
-$\left( \frac { 1 } { 64 } \right) ^ { - 1 / 3 }$

Accepted Answer

A)  $- \frac { 1 } { 4 }$ 
B)  $\frac { 1 } { 4 }$ 
C)  $- 4$ 
D)  4 
A)  $- \frac { 1 } { 4 }$ 
B)  $\frac { 1 } { 4 }$ 
C)  $- 4$ 
D)  4

Question 5

Use the product rule to multiply. Assume all variables represent positive real numbers.
-$\sqrt { 5 } \cdot \sqrt { 5 }$

Accepted Answer

A)  $\sqrt { 25 }$ 
B)  $\sqrt { 5 }$ 
C)  $\sqrt { 10 }$ 
D)  5 
A)  $\sqrt { 25 }$ 
B)  $\sqrt { 5 }$ 
C)  $\sqrt { 10 }$ 
D)  5

Question 6

Raise to the power or find the root. Assume that all variables represent positive real numbers. Write with only positive
exponents.
-$\left( \frac { 27 x ^ { 3 } } { 125 } \right) ^ { 2 / 3 }$

Accepted Answer

A)  $\frac { 27 x ^ { 3 } } { 5 }$ 
B)  $\frac { 9 } { 25 }$ 
C)  $\frac { 9 x ^ { 2 } } { 25 }$ 
D)  $\frac { 3 x ^ { 1 } } { 25 }$ 
A)  $\frac { 27 x ^ { 3 } } { 5 }$ 
B)  $\frac { 9 } { 25 }$ 
C)  $\frac { 9 x ^ { 2 } } { 25 }$ 
D)  $\frac { 3 x ^ { 1 } } { 25 }$

Question 7

Write in terms of i.
-$- \sqrt { - 296 }$

Accepted Answer

A)  $2 \mathrm { i } \sqrt { 74 }$ 
B)  $2 \sqrt { 74 }$ 
C)  $- 2 \mathrm { i } \sqrt { 74 }$ 
D)  $- 2 \sqrt { 74 }$ 
A)  $2 \mathrm { i } \sqrt { 74 }$ 
B)  $2 \sqrt { 74 }$ 
C)  $- 2 \mathrm { i } \sqrt { 74 }$ 
D)  $- 2 \sqrt { 74 }$

Question 8

Solve.
-$x - \sqrt { 26 x + 39 } = - 8$

Accepted Answer

A)  $- 5$ 
B)  $- 4$ 
C)  5 
D)  7 
A)  $- 5$ 
B)  $- 4$ 
C)  5 
D)  7

Question 9

Multiply or divide.
-$\sqrt { - 3 } \cdot \sqrt { - 5 }$

Accepted Answer

A)  $\sqrt { 15 }$ 
B)  $- \mathrm { i } \sqrt { 15 }$ 
C)  $\mathrm { i } \sqrt { 15 }$ 
D)  $- \sqrt { 15 }$ 
A)  $\sqrt { 15 }$ 
B)  $- \mathrm { i } \sqrt { 15 }$ 
C)  $\mathrm { i } \sqrt { 15 }$ 
D)  $- \sqrt { 15 }$

Question 10

Perform the indicated operation. Assume that all variables represent positive real numbers.
-$\sqrt { 252 x ^ { 3 } } - 2 \sqrt { 28 x ^ { 3 } }$

Accepted Answer

A)  $2 x \sqrt { 7 x }$ 
B)  $2 \sqrt { 7 x ^ { 3 } }$ 
C)  $- 2 \sqrt { 224 \mathrm { x } ^ { 3 } }$ 
D)  $10 x \sqrt { 7 x }$ 
A)  $2 x \sqrt { 7 x }$ 
B)  $2 \sqrt { 7 x ^ { 3 } }$ 
C)  $- 2 \sqrt { 224 \mathrm { x } ^ { 3 } }$ 
D)  $10 x \sqrt { 7 x }$

Question 11

Find the power of i.
-$( - 4 i ) ^ { 7 }$

Accepted Answer

A)  $- 1024$ 
B)  $- 16,384 i$ 
C)  $16,384 \mathrm { i }$ 
D)  1024 
A)  $- 1024$ 
B)  $- 16,384 i$ 
C)  $16,384 \mathrm { i }$ 
D)  1024

Question 12

Multiply, and then simplify if possible. Assume all variables represent positive real numbers.
-$( \sqrt { 11 } + \sqrt { 6 } ) ( \sqrt { 11 } - \sqrt { 6 } )$

Accepted Answer

A)  $11 - 2 \sqrt { 6 }$ 
B)  $11 - 2 \sqrt { 11 }$ 
C)  5 
D)  17 
A)  $11 - 2 \sqrt { 6 }$ 
B)  $11 - 2 \sqrt { 11 }$ 
C)  5 
D)  17

Question 13

Find the distance between the pair of points.
-$( 3.5 , - 4.3 )$ and $( - 8.6 , - 5.7 )$
Approximate the distance to two decimal places.

Accepted Answer

A)  $15.7$ units 
B)  $11.23$ units 
C)  $12.18$ units 
D)  $5.29$ units 
A)  $15.7$ units 
B)  $11.23$ units 
C)  $12.18$ units 
D)  $5.29$ units

Question 14

Solve.
-$$\sqrt { 4 x + 5 } - 9 = 0$$

Accepted Answer

A)  19 
B)  304 
C)  $\frac { 1 } { 19 }$ 
D)  $\varnothing$ 
A)  19 
B)  304 
C)  $\frac { 1 } { 19 }$ 
D)  $\varnothing$

Question 15

Perform the indicated operation. Write the result in the form a + bi.
-$( 3 \mathrm { i } ) ( 7 \mathrm { i } )$

Accepted Answer

A)  $21 \mathrm { i }$ 
B)  21 
C)  $- 21 \mathrm { i }$ 
D)  $- 21$ 
A)  $21 \mathrm { i }$ 
B)  21 
C)  $- 21 \mathrm { i }$ 
D)  $- 21$

Question 16

Use a calculator to approximate the square root to 3 decimal places. Check to see that the approximation is reasonable.
-$\sqrt { 7 }$

Accepted Answer

A)  $2.651$ 
B)  $7.000$ 
C)  $2.643$ 
D)  $2.646$ 
A)  $2.651$ 
B)  $7.000$ 
C)  $2.643$ 
D)  $2.646$

Question 17

Multiply or divide.
-$\frac { \sqrt { 9 } } { \sqrt { - 10 } }$

Accepted Answer

A)  $\frac { 3 \sqrt { 10 } } { 10 }$ 
B)  $\frac { - 3 \sqrt { 10 } } { 10 }$ 
C)  $\frac { 3 \mathrm { i } \sqrt { 10 } } { 10 }$ 
D)  $\frac { - 3 \mathrm { i } \sqrt { 10 } } { 10 }$ 
A)  $\frac { 3 \sqrt { 10 } } { 10 }$ 
B)  $\frac { - 3 \sqrt { 10 } } { 10 }$ 
C)  $\frac { 3 \mathrm { i } \sqrt { 10 } } { 10 }$ 
D)  $\frac { - 3 \mathrm { i } \sqrt { 10 } } { 10 }$

Question 18

Use a calculator to approximate the number to three decimal places.
-$434 ^ { - 2 / 3 }$

Accepted Answer

A)  $0.019$ 
B)  $0.014$ 
C)  $0.017$ 
D)  $0.016$ 
A)  $0.019$ 
B)  $0.014$ 
C)  $0.017$ 
D)  $0.016$

Question 19

Find the square root. Assume that all variables represent nonnegative real numbers.
-$\sqrt { 0.36 }$

Accepted Answer

A)  $0.006$ 
B)  $0.6$ 
C)  6 
D)  $0.06$ 
A)  $0.006$ 
B)  $0.6$ 
C)  6 
D)  $0.06$

Question 20

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers.
-$\frac { 8 x } { \sqrt [ 5 ] { 9 x ^ { 18 } y ^ { 12 } } }$

Accepted Answer

A)  $\frac { 8 \sqrt [ 5 ] { 9 x ^ { 18 } y ^ { 12 } } } { 9 x ^ { 18 } y ^ { 12 } }$ 
B)  $\frac { 8 \sqrt [ 5 ] { 27 x ^ { 2 } y ^ { 3 } } } { 3 x ^ { 3 } y ^ { 2 } }$ 
C)  $\frac { 8 \sqrt [ 5 ] { 27 x ^ { 2 } y ^ { 3 } } } { 3 x ^ { 4 } y ^ { 3 } }$ 
D)  $\frac { 8 \sqrt [ 5 ] { 9 x ^ { 3 } y ^ { 2 } } } { 3 x ^ { 3 } y ^ { 2 } }$ 
A)  $\frac { 8 \sqrt [ 5 ] { 9 x ^ { 18 } y ^ { 12 } } } { 9 x ^ { 18 } y ^ { 12 } }$ 
B)  $\frac { 8 \sqrt [ 5 ] { 27 x ^ { 2 } y ^ { 3 } } } { 3 x ^ { 3 } y ^ { 2 } }$ 
C)  $\frac { 8 \sqrt [ 5 ] { 27 x ^ { 2 } y ^ { 3 } } } { 3 x ^ { 4 } y ^ { 3 } }$ 
D)  $\frac { 8 \sqrt [ 5 ] { 9 x ^ { 3 } y ^ { 2 } } } { 3 x ^ { 3 } y ^ { 2 } }$

Write in terms of i. - $\sqrt { - 400 }$

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers. - $\frac { 8 } { \sqrt [ 3 ] { y } }$

Use the Pythagorean theorem to find the unknown side of the right triangle. -

Raise to the power or find the root. Assume that all variables represent positive real numbers. Write with only positive exponents. - $\left( \frac { 1 } { 64 } \right) ^ { - 1 / 3 }$

Use the product rule to multiply. Assume all variables represent positive real numbers. - $\sqrt { 5 } \cdot \sqrt { 5 }$

Raise to the power or find the root. Assume that all variables represent positive real numbers. Write with only positive exponents. - $\left( \frac { 27 x ^ { 3 } } { 125 } \right) ^ { 2 / 3 }$

Write in terms of i. - $- \sqrt { - 296 }$

Solve. - $x - \sqrt { 26 x + 39 } = - 8$

Multiply or divide. - $\sqrt { - 3 } \cdot \sqrt { - 5 }$

Perform the indicated operation. Assume that all variables represent positive real numbers. - $\sqrt { 252 x ^ { 3 } } - 2 \sqrt { 28 x ^ { 3 } }$

Find the power of i. - $( - 4 i ) ^ { 7 }$

Multiply, and then simplify if possible. Assume all variables represent positive real numbers. - $( \sqrt { 11 } + \sqrt { 6 } ) ( \sqrt { 11 } - \sqrt { 6 } )$

Find the distance between the pair of points. - $( 3.5 , - 4.3 )$ and $( - 8.6 , - 5.7 )$ Approximate the distance to two decimal places.

Solve. - $\sqrt { 4 x + 5 } - 9 = 0$

Perform the indicated operation. Write the result in the form a + bi. - $( 3 \mathrm { i } ) ( 7 \mathrm { i } )$

Use a calculator to approximate the square root to 3 decimal places. Check to see that the approximation is reasonable. - $\sqrt { 7 }$

Multiply or divide. - $\frac { \sqrt { 9 } } { \sqrt { - 10 } }$

Use a calculator to approximate the number to three decimal places. - $434 ^ { - 2 / 3 }$

Find the square root. Assume that all variables represent nonnegative real numbers. - $\sqrt { 0.36 }$

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers. - $\frac { 8 x } { \sqrt [ 5 ] { 9 x ^ { 18 } y ^ { 12 } } }$

Real Numbers and Algebraic Expressions

Equations, Inequalities, and Problem Solving

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Polynomial Functions

Rational Expressions

Quadratic Equations and Functions

Exponential and Logarithmic Functions

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Filters

Exam 7: Rational Exponents, Radicals, and Complex Numbers

Write in terms of i. - −400\sqrt { - 400 }−400​

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers. - 8y3\frac { 8 } { \sqrt [ 3 ] { y } }3y​8​

Use the Pythagorean theorem to find the unknown side of the right triangle. -

Raise to the power or find the root. Assume that all variables represent positive real numbers. Write with only positive exponents. - (164)−1/3\left( \frac { 1 } { 64 } \right) ^ { - 1 / 3 }(641​)−1/3

Use the product rule to multiply. Assume all variables represent positive real numbers. - 5⋅5\sqrt { 5 } \cdot \sqrt { 5 }5​⋅5​

Raise to the power or find the root. Assume that all variables represent positive real numbers. Write with only positive exponents. - (27x3125)2/3\left( \frac { 27 x ^ { 3 } } { 125 } \right) ^ { 2 / 3 }(12527x3​)2/3

Write in terms of i. - −−296- \sqrt { - 296 }−−296​

Solve. - x−26x+39=−8x - \sqrt { 26 x + 39 } = - 8x−26x+39​=−8

Multiply or divide. - −3⋅−5\sqrt { - 3 } \cdot \sqrt { - 5 }−3​⋅−5​

Perform the indicated operation. Assume that all variables represent positive real numbers. - 252x3−228x3\sqrt { 252 x ^ { 3 } } - 2 \sqrt { 28 x ^ { 3 } }252x3​−228x3​

Find the power of i. - (−4i)7( - 4 i ) ^ { 7 }(−4i)7

Multiply, and then simplify if possible. Assume all variables represent positive real numbers. - (11+6)(11−6)( \sqrt { 11 } + \sqrt { 6 } ) ( \sqrt { 11 } - \sqrt { 6 } )(11​+6​)(11​−6​)

Find the distance between the pair of points. - (3.5,−4.3)( 3.5 , - 4.3 )(3.5,−4.3) and (−8.6,−5.7)( - 8.6 , - 5.7 )(−8.6,−5.7) Approximate the distance to two decimal places.

Solve. - 4x+5−9=0\sqrt { 4 x + 5 } - 9 = 04x+5​−9=0

Perform the indicated operation. Write the result in the form a + bi. - (3i)(7i)( 3 \mathrm { i } ) ( 7 \mathrm { i } )(3i)(7i)

Use a calculator to approximate the square root to 3 decimal places. Check to see that the approximation is reasonable. - 7\sqrt { 7 }7​

Multiply or divide. - 9−10\frac { \sqrt { 9 } } { \sqrt { - 10 } }−10​9​​

Use a calculator to approximate the number to three decimal places. - 434−2/3434 ^ { - 2 / 3 }434−2/3

Find the square root. Assume that all variables represent nonnegative real numbers. - 0.36\sqrt { 0.36 }0.36​

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers. - 8x9x18y125\frac { 8 x } { \sqrt [ 5 ] { 9 x ^ { 18 } y ^ { 12 } } }59x18y12​8x​