Question 1

Use a calculator to approximate the number to three decimal places.
-$\sqrt { 598 }$

Accepted Answer

A)  $598.000$ 
B)  $24.454$ 
C)  $24.451$ 
D)  $24.459$ 
A)  $598.000$ 
B)  $24.454$ 
C)  $24.451$ 
D)  $24.459$

Question 2

Multiply or divide.
-$$\sqrt { 2 } \cdot \sqrt { - 125 }$$

Accepted Answer

A)  $5 \mathrm { i } \sqrt { 10 }$ 
B)  $- 250$ 
C)  $- 5 \mathrm { i } \sqrt { 10 }$ 
D)  250 
A)  $5 \mathrm { i } \sqrt { 10 }$ 
B)  $- 250$ 
C)  $- 5 \mathrm { i } \sqrt { 10 }$ 
D)  250

Question 3

Add or subtract. Assume all variables represent positive real numbers.
-$\sqrt { \frac { 3 } { 36 } } + \sqrt { \frac { 48 } { 25 } }$

Accepted Answer

A)  $\frac { 29 \sqrt { 3 } } { 6 }$ 
B)  $\frac { 3 \sqrt { 29 } } { 30 }$ 
C)  $\frac { 29 \sqrt { 3 } } { 30 }$ 
D)  $\frac { - 19 \sqrt { 3 } } { 30 }$ 
A)  $\frac { 29 \sqrt { 3 } } { 6 }$ 
B)  $\frac { 3 \sqrt { 29 } } { 30 }$ 
C)  $\frac { 29 \sqrt { 3 } } { 30 }$ 
D)  $\frac { - 19 \sqrt { 3 } } { 30 }$

Question 4

Simplify. Assume that all variables represent positive real numbers.
-$\sqrt { 26 }$

Accepted Answer

A)  $13 \sqrt { 2 }$ 
B)  $2 \sqrt { 13 }$ 
C)  $\sqrt { 26 }$ 
D)  13 
A)  $13 \sqrt { 2 }$ 
B)  $2 \sqrt { 13 }$ 
C)  $\sqrt { 26 }$ 
D)  13

Question 5

Find the power of i.
-$\mathrm { i } ^ { 9 }$

Accepted Answer

A)  1 
B)  $i$ 
C)  $- 1$ 
D)  $- \mathrm { i }$ 
A)  1 
B)  $i$ 
C)  $- 1$ 
D)  $- \mathrm { i }$

Question 6

Solve.
-$$\sqrt { 2 x + 7 } + 2 = 0$$

Accepted Answer

A)  $- 6$ 
B)  $- \frac { 2 } { 3 }$ 
C) $ - \frac { 3 } { 2 }$ 
D)  $\varnothing$ 
A)  $- 6$ 
B)  $- \frac { 2 } { 3 }$ 
C) $ - \frac { 3 } { 2 }$ 
D)  $\varnothing$

Question 7

Use the quotient rule to divide and simplify.
-$\sqrt [ 3 ] { \frac { x ^ { 2 } } { 16 } }$

Accepted Answer

A)  $\frac { x \sqrt { x } } { 2 }$ 
B)  $\frac { \sqrt [ 3 ] { x ^ { 2 } } } { 2 }$ 
C)  $\frac { x \sqrt { x } } { 2 \sqrt { 4 } }$ 
D)  $\frac { \sqrt [ 3 ] { x ^ { 2 } } } { 2 \sqrt [ 3 ] { 2 } }$ 
A)  $\frac { x \sqrt { x } } { 2 }$ 
B)  $\frac { \sqrt [ 3 ] { x ^ { 2 } } } { 2 }$ 
C)  $\frac { x \sqrt { x } } { 2 \sqrt { 4 } }$ 
D)  $\frac { \sqrt [ 3 ] { x ^ { 2 } } } { 2 \sqrt [ 3 ] { 2 } }$

Question 8

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

-Theــــــــــــــــــــــــــــ formula is $\left( \frac { x _ { 1 } + x _ { 2 } } { 2 } , \frac { y _ { 1 } + y _ { 2 } } { 2 } \right)$.

Accepted Answer

A)  distance 
B)  midpoint 
C)  index 
D)  conjugate 
A)  distance 
B)  midpoint 
C)  index 
D)  conjugate

Question 9

Add or subtract. Assume all variables represent positive real numbers.
-$4 \sqrt { 3 } + 2 \sqrt { 27 }$

Accepted Answer

A)  $10 \sqrt { 3 }$ 
B)  $- 10 \sqrt { 3 }$ 
C)  $6 \sqrt { 3 }$ 
D)  $2 \sqrt { 3 }$ 
A)  $10 \sqrt { 3 }$ 
B)  $- 10 \sqrt { 3 }$ 
C)  $6 \sqrt { 3 }$ 
D)  $2 \sqrt { 3 }$

Question 10

Simplify. Assume that all variables represent positive real numbers.
-$\frac { \sqrt { 1008 x ^ { 7 } } } { \sqrt { 7 x } }$

Accepted Answer

A)  $12 \sqrt { x ^ { 7 } }$ 
B)  $12 x ^ { 6 }$ 
C)  $12 x ^ { 3 } \sqrt { 7 }$ 
D)  $12 x ^ { 3 }$ 
A)  $12 \sqrt { x ^ { 7 } }$ 
B)  $12 x ^ { 6 }$ 
C)  $12 x ^ { 3 } \sqrt { 7 }$ 
D)  $12 x ^ { 3 }$

Question 11

Use radical notation to write the expression. Simplify if possible.
-$$\left( \frac { 9 } { 16 } \right) ^ { 1 / 2 }$$

Accepted Answer

A)  $\frac { 2 } { 5 }$ 
B)  $\frac { 3 } { 4 }$ 
C)  $\frac { 3 } { 5 }$ 
D)  $\frac { 1 } { 2 }$ 
A)  $\frac { 2 } { 5 }$ 
B)  $\frac { 3 } { 4 }$ 
C)  $\frac { 3 } { 5 }$ 
D)  $\frac { 1 } { 2 }$

Question 12

Write with positive exponents. Simplify if possible.
-$16 ^ { - 3 / 2 }$

Accepted Answer

A)  $- 64$ 
B)  $\frac { 1 } { 64 }$ 
C)  $- \frac { 1 } { 64 }$ 
D)  64 
A)  $- 64$ 
B)  $\frac { 1 } { 64 }$ 
C)  $- \frac { 1 } { 64 }$ 
D)  64

Question 13

Use radical notation to write the expression. Simplify if possible.
-$$91 / 2$$

Accepted Answer

A)  1.5 
B)  12 
C)  6 
D)  3 
A)  1.5 
B)  12 
C)  6 
D)  3

Question 14

Use the quotient rule to divide and simplify.
-$\sqrt { \frac { 11 } { 81 } }$

Accepted Answer

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

Question 15

Add or subtract. Assume all variables represent positive real numbers.
-$$\sqrt [ 3 ] { 27 y } - \sqrt [ 3 ] { 128 y }$$

Accepted Answer

A)  $4 \sqrt [ 3 ] { 2 y } - 3 \sqrt [ 3 ] { y }$ 
B)  $3 \sqrt [ 3 ] { y } - 4 \sqrt [ 3 ] { 2 y }$ 
C)  $3 - 4 \sqrt [ 3 ] { 2 }$ 
D)  $7 \sqrt [ 3 ] { y }$ 
A)  $4 \sqrt [ 3 ] { 2 y } - 3 \sqrt [ 3 ] { y }$ 
B)  $3 \sqrt [ 3 ] { y } - 4 \sqrt [ 3 ] { 2 y }$ 
C)  $3 - 4 \sqrt [ 3 ] { 2 }$ 
D)  $7 \sqrt [ 3 ] { y }$

Question 16

Use rational exponents to write as a single radical expression.
-$\sqrt [ 3 ] { x } \cdot \sqrt { x }$

Accepted Answer

A)  $x ^ { 5 }$ 
B)  $\sqrt [ 6 ] { x ^ { 5 } }$ 
C)  $\sqrt [ 3 ] { \mathrm { x } ^ { 2 } }$ 
D)  $\sqrt { \mathrm { x } ^ { 5 } }$ 
A)  $x ^ { 5 }$ 
B)  $\sqrt [ 6 ] { x ^ { 5 } }$ 
C)  $\sqrt [ 3 ] { \mathrm { x } ^ { 2 } }$ 
D)  $\sqrt { \mathrm { x } ^ { 5 } }$

Question 17

Add or subtract. Assume all variables represent positive real numbers.
-$- 2 \sqrt { 8 } - 2 \sqrt { 18 } - 8 \sqrt { 32 }$

Accepted Answer

A)  $- 12 \sqrt { 2 }$ 
B)  $- 2 \sqrt { 2 }$ 
C)  $- 42 \sqrt { 2 }$ 
D)  $12 \sqrt { 2 }$ 
A)  $- 12 \sqrt { 2 }$ 
B)  $- 2 \sqrt { 2 }$ 
C)  $- 42 \sqrt { 2 }$ 
D)  $12 \sqrt { 2 }$

Question 18

Use rational exponents to simplify. Assume that all variables represent positive real numbers.
-$\sqrt [ 15 ] { \mathrm { x } ^ { 12 } \mathrm { y } ^ { 9 } }$

Accepted Answer

A)  $\sqrt [ 5 ] { x ^ { 4 } y }$ 
B)  $\sqrt [ 3 ] { x ^ { 4 } y ^ { 3 } }$ 
C)  $\sqrt [ 5 ] { x ^ { 4 } y ^ { 3 } }$ 
D)  $\sqrt [ 5 ] { x y ^ { 3 } }$ 
A)  $\sqrt [ 5 ] { x ^ { 4 } y }$ 
B)  $\sqrt [ 3 ] { x ^ { 4 } y ^ { 3 } }$ 
C)  $\sqrt [ 5 ] { x ^ { 4 } y ^ { 3 } }$ 
D)  $\sqrt [ 5 ] { x y ^ { 3 } }$

Question 19

Solve.
-$$\sqrt { 8 x + 4 } = \sqrt { 6 x + 1 } - 1$$

Accepted Answer

A)  0,8 
B)  4 
C)  0,4 
D)  $\varnothing$ 
A)  0,8 
B)  4 
C)  0,4 
D)  $\varnothing$

Question 20

Use radical notation to write the expression. Simplify if possible.
-$7 x ^ { 3 / 10 }$

Accepted Answer

A)  $\sqrt [ 10 ] { 343 x ^ { 3 } }$ 
B)  $\sqrt [ 10 ] { 7 x ^ { 3 } }$ 
C)  $7 \sqrt [ 10 ] { \mathrm { x } ^ { 3 } }$ 
D)  $\sqrt [ 3 ] { 7 x ^ { 10 } }$ 
A)  $\sqrt [ 10 ] { 343 x ^ { 3 } }$ 
B)  $\sqrt [ 10 ] { 7 x ^ { 3 } }$ 
C)  $7 \sqrt [ 10 ] { \mathrm { x } ^ { 3 } }$ 
D)  $\sqrt [ 3 ] { 7 x ^ { 10 } }$

Use a calculator to approximate the number to three decimal places. - $\sqrt { 598 }$

Multiply or divide. - $\sqrt { 2 } \cdot \sqrt { - 125 }$

Add or subtract. Assume all variables represent positive real numbers. - $\sqrt { \frac { 3 } { 36 } } + \sqrt { \frac { 48 } { 25 } }$

Simplify. Assume that all variables represent positive real numbers. - $\sqrt { 26 }$

Find the power of i. - $\mathrm { i } ^ { 9 }$

Solve. - $\sqrt { 2 x + 7 } + 2 = 0$

Use the quotient rule to divide and simplify. - $\sqrt [ 3 ] { \frac { x ^ { 2 } } { 16 } }$

Add or subtract. Assume all variables represent positive real numbers. - $4 \sqrt { 3 } + 2 \sqrt { 27 }$

Simplify. Assume that all variables represent positive real numbers. - $\frac { \sqrt { 1008 x ^ { 7 } } } { \sqrt { 7 x } }$

Use radical notation to write the expression. Simplify if possible. - $\left( \frac { 9 } { 16 } \right) ^ { 1 / 2 }$

Write with positive exponents. Simplify if possible. - $16 ^ { - 3 / 2 }$

Use radical notation to write the expression. Simplify if possible. - $91 / 2$

Use the quotient rule to divide and simplify. - $\sqrt { \frac { 11 } { 81 } }$

Add or subtract. Assume all variables represent positive real numbers. - $\sqrt [ 3 ] { 27 y } - \sqrt [ 3 ] { 128 y }$

Use rational exponents to write as a single radical expression. - $\sqrt [ 3 ] { x } \cdot \sqrt { x }$

Add or subtract. Assume all variables represent positive real numbers. - $- 2 \sqrt { 8 } - 2 \sqrt { 18 } - 8 \sqrt { 32 }$

Use rational exponents to simplify. Assume that all variables represent positive real numbers. - $\sqrt [ 15 ] { \mathrm { x } ^ { 12 } \mathrm { y } ^ { 9 } }$

Solve. - $\sqrt { 8 x + 4 } = \sqrt { 6 x + 1 } - 1$

Use radical notation to write the expression. Simplify if possible. - $7 x ^ { 3 / 10 }$

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

Use a calculator to approximate the number to three decimal places. - 598\sqrt { 598 }598​

Multiply or divide. - 2⋅−125\sqrt { 2 } \cdot \sqrt { - 125 }2​⋅−125​

Add or subtract. Assume all variables represent positive real numbers. - 336+4825\sqrt { \frac { 3 } { 36 } } + \sqrt { \frac { 48 } { 25 } }363​​+2548​​

Simplify. Assume that all variables represent positive real numbers. - 26\sqrt { 26 }26​

Find the power of i. - i9\mathrm { i } ^ { 9 }i9

Solve. - 2x+7+2=0\sqrt { 2 x + 7 } + 2 = 02x+7​+2=0

Use the quotient rule to divide and simplify. - x2163\sqrt [ 3 ] { \frac { x ^ { 2 } } { 16 } }316x2​​

Fill in the blank with one of the words or phrases listed below. -Theــــــــــــــــــــــــــــ formula is (x1+x22,y1+y22)\left( \frac { x _ { 1 } + x _ { 2 } } { 2 } , \frac { y _ { 1 } + y _ { 2 } } { 2 } \right)(2x1​+x2​​,2y1​+y2​​) .

Add or subtract. Assume all variables represent positive real numbers. - 43+2274 \sqrt { 3 } + 2 \sqrt { 27 }43​+227​

Simplify. Assume that all variables represent positive real numbers. - 1008x77x\frac { \sqrt { 1008 x ^ { 7 } } } { \sqrt { 7 x } }7x​1008x7​​

Use radical notation to write the expression. Simplify if possible. - (916)1/2\left( \frac { 9 } { 16 } \right) ^ { 1 / 2 }(169​)1/2

Write with positive exponents. Simplify if possible. - 16−3/216 ^ { - 3 / 2 }16−3/2

Use radical notation to write the expression. Simplify if possible. - 91/291 / 291/2

Use the quotient rule to divide and simplify. - 1181\sqrt { \frac { 11 } { 81 } }8111​​

Add or subtract. Assume all variables represent positive real numbers. - 27y3−128y3\sqrt [ 3 ] { 27 y } - \sqrt [ 3 ] { 128 y }327y​−3128y​

Use rational exponents to write as a single radical expression. - x3⋅x\sqrt [ 3 ] { x } \cdot \sqrt { x }3x​⋅x​

Add or subtract. Assume all variables represent positive real numbers. - −28−218−832- 2 \sqrt { 8 } - 2 \sqrt { 18 } - 8 \sqrt { 32 }−28​−218​−832​

Use rational exponents to simplify. Assume that all variables represent positive real numbers. - x12y915\sqrt [ 15 ] { \mathrm { x } ^ { 12 } \mathrm { y } ^ { 9 } }15x12y9​

Solve. - 8x+4=6x+1−1\sqrt { 8 x + 4 } = \sqrt { 6 x + 1 } - 18x+4​=6x+1​−1

Use radical notation to write the expression. Simplify if possible. - 7x3/107 x ^ { 3 / 10 }7x3/10