Question 1

Add or subtract the complex numbers
-$(4+8 \mathrm{i})-(-8+\mathrm{i})$

Accepted Answer

A)  $12+7 i$ 
B)  $12-7 \mathrm{i}$ 
C)  $-12-7 \mathrm{i}$ 
D)  $-4+9 \mathrm{i}$ 
A)  $12+7 i$ 
B)  $12-7 \mathrm{i}$ 
C)  $-12-7 \mathrm{i}$ 
D)  $-4+9 \mathrm{i}$ A

Question 2

Simplify the expression. Assume all variables represent nonnegative real numbers.
-$\left(b^{7 / 5}\right)^{5}$

Accepted Answer

A)  $b^{7}$ 
B)  $b^{12 / 5}$ 
C)  $b^{7 / 25}$ 
D)  $b^{1 / 5}$ 
A)  $b^{7}$ 
B)  $b^{12 / 5}$ 
C)  $b^{7 / 25}$ 
D)  $b^{1 / 5}$ A

Question 3

Rewrite the radical expression using rational exponents. A ssume all variables represent nonnegative real numbers.
-$\sqrt{\mathrm{x}^{9}}$

Accepted Answer

A)  $x 9 / 2$ 
B)  $-x^{2 / 9}$ 
C)  $x^{-2 / 9}$ 
D)  $x^{-9 / 2}$ 
A)  $x 9 / 2$ 
B)  $-x^{2 / 9}$ 
C)  $x^{-2 / 9}$ 
D)  $x^{-9 / 2}$ A

Question 4

Multiply
-$(3 \sqrt{2}+4 \sqrt{5})(4 \sqrt{11}-5 \sqrt{17})$

Accepted Answer

A)  $12 \sqrt{22}-15 \sqrt{34}+16 \sqrt{55}-5 \sqrt{85}$ 
B)  $12 \sqrt{22}-5 \sqrt{34}+16 \sqrt{55}-20 \sqrt{85}$ 
C)  $12 \sqrt{22}-15 \sqrt{34}+4 \sqrt{55}-20 \sqrt{85}$ 
D)  $12 \sqrt{22}-15 \sqrt{34}+16 \sqrt{55}-20 \sqrt{85}$ 
A)  $12 \sqrt{22}-15 \sqrt{34}+16 \sqrt{55}-5 \sqrt{85}$ 
B)  $12 \sqrt{22}-5 \sqrt{34}+16 \sqrt{55}-20 \sqrt{85}$ 
C)  $12 \sqrt{22}-15 \sqrt{34}+4 \sqrt{55}-20 \sqrt{85}$ 
D)  $12 \sqrt{22}-15 \sqrt{34}+16 \sqrt{55}-20 \sqrt{85}$

Question 5

Multiply.
-$4 \mathrm{i} \cdot \mathrm{-}$1i

Accepted Answer

A)  $4 \mathrm{i}$ 
B)  -4 
C)  $-4 \mathrm{i}$ 
D)  4 
A)  $4 \mathrm{i}$ 
B)  -4 
C)  $-4 \mathrm{i}$ 
D)  4

Question 6

Rationalize the denominator and simplify. A ssume all variables represent nonnegative real numbers.
-$\sqrt{\frac{7}{27 \mathrm{xy}^{2}}}$

Accepted Answer

A)  $\frac{\sqrt{21 x}}{9 x y}$ 
B)  $\frac{\sqrt{21}}{9 y \sqrt{x}}$ 
C)  $\frac{7 \sqrt{3 x}}{9 x y}$ 
D)  $\frac{\sqrt{21 x y}}{9 x y}$ 
A)  $\frac{\sqrt{21 x}}{9 x y}$ 
B)  $\frac{\sqrt{21}}{9 y \sqrt{x}}$ 
C)  $\frac{7 \sqrt{3 x}}{9 x y}$ 
D)  $\frac{\sqrt{21 x y}}{9 x y}$

Question 7

Find the domain of the function. Express the answer in interval notation.
-$f(x)=\sqrt{2 x+2}$

Accepted Answer

A)  $[-1, \infty)$ 
B)  $(-1, \infty)$ 
C)  $(1, \infty)$ 
D)  $(-\infty,-1)$ 
A)  $[-1, \infty)$ 
B)  $(-1, \infty)$ 
C)  $(1, \infty)$ 
D)  $(-\infty,-1)$

Question 8

A ssume all variables represent nonnegative real numbers.
-$\sqrt{11}(\sqrt{11}-\sqrt{55})$

Accepted Answer

A)  $11-\sqrt{605}$ 
B)  $11+11 \sqrt{5}$ 
C)  $11-5 \sqrt{11}$ 
D)  $11-11 \sqrt{5}$ 
A)  $11-\sqrt{605}$ 
B)  $11+11 \sqrt{5}$ 
C)  $11-5 \sqrt{11}$ 
D)  $11-11 \sqrt{5}$

Question 9

Use the Babylonian method to approximate the given square root to the nearest thousandth.
-$\sqrt{600}$

Accepted Answer

A)  24.454 
B)  24.474 
C)  24.495 
D)  24.597 
A)  24.454 
B)  24.474 
C)  24.495 
D)  24.597

Question 10

Simplify the radical expression. If appropriate, include absolute values.
-$\sqrt{196 y^{6}}$

Accepted Answer

A)  $14 y^{3}$ 
B)  $14|\mathrm{y}|$ 
C)  $14 y^{2}$ 
D)  $14\left|y^{3}\right|$ 
A)  $14 y^{3}$ 
B)  $14|\mathrm{y}|$ 
C)  $14 y^{2}$ 
D)  $14\left|y^{3}\right|$

Question 11

Choose the one alternative that best completes the statement or answers thequestion.
Express in terms of i.
-$\sqrt{-81}$

Accepted Answer

A)  $\pm 9$ 
B)  - $9 \mathrm{i}$ 
C)  $9 \mathrm{i}$ 
D)  $-\mathrm{i} \sqrt{9}$ 
A)  $\pm 9$ 
B)  - $9 \mathrm{i}$ 
C)  $9 \mathrm{i}$ 
D)  $-\mathrm{i} \sqrt{9}$

Question 12

Simplify the expression. Assume all variables represent nonnegative real numbers.
-$z^{-2 / 7} \cdot z^{3 / 7}$

Accepted Answer

A)  $z^{6 / 7}$ 
B)  $\mathrm{z}^{7}$ 
C)  $z^{1 / 7}$ 
D)  $z^{7 / 6}$ 
A)  $z^{6 / 7}$ 
B)  $\mathrm{z}^{7}$ 
C)  $z^{1 / 7}$ 
D)  $z^{7 / 6}$

Question 13

A student tries to solve $\sqrt{\mathrm{x}+7}=\sqrt{\mathrm{x}}+4$ by squaring both sides and gets $\mathrm{x}+7=\mathrm{x}+16$.
Why is this not correct?

Accepted Answer

Squaring the right s

Question 14

Add or subtract the complex numbers
-$(-7+2 \mathrm{i})-5$

Accepted Answer

A)  -2 - $2 \mathrm{i}$ 
B)  $-2+2 i$ 
C)  $-12+2 \mathrm{i}$ 
D)  $12-2 \mathrm{i}$ 
A)  -2 - $2 \mathrm{i}$ 
B)  $-2+2 i$ 
C)  $-12+2 \mathrm{i}$ 
D)  $12-2 \mathrm{i}$

Question 15

Find the domain of the function. Express the answer in interval notation.
-$f(x)=\sqrt[4]{x-19}$

Accepted Answer

A)  $[19, \infty)$ 
B)  $[0, \infty)$ 
C)  $[-19, \infty)$ 
D)  $(-\infty, \infty)$ 
A)  $[19, \infty)$ 
B)  $[0, \infty)$ 
C)  $[-19, \infty)$ 
D)  $(-\infty, \infty)$

Question 16

Simplify.
-$\frac{\sqrt{10}}{\sqrt{2}}$

Accepted Answer

A)  $\sqrt{2}$ 
B)  5 
C)  $\sqrt{5}$ 
D)  2 
A)  $\sqrt{2}$ 
B)  5 
C)  $\sqrt{5}$ 
D)  2

Question 17

$5 \sqrt[3]{3}-9 \sqrt{6}+2 \sqrt[3]{3}+7 \sqrt{6}$

Accepted Answer

A)  $7 \sqrt[3]{6}-2 \sqrt{12}$ 
B)  $7 \sqrt[3]{3}-2 \sqrt{6}$ 
C)  $5 \sqrt{18}$ 
D)  $7 \sqrt{3}-2 \sqrt{6}$ 
A)  $7 \sqrt[3]{6}-2 \sqrt{12}$ 
B)  $7 \sqrt[3]{3}-2 \sqrt{6}$ 
C)  $5 \sqrt{18}$ 
D)  $7 \sqrt{3}-2 \sqrt{6}$

Question 18

The length a spring is stretched from its natural length with work, W foot- pounds, is given by $\mathrm{L}=\sqrt{\frac{2 \mathrm{~W}}{\mathrm{k}}}$
Where $\mathrm{k}$ is a constant for the given spring. If a certain spring has a constant of 65.7, and the spring is to be stretched 2.6 feet from its natural length, how much work will be necessary? Round to the nearest tenth of a foot- pound.

Accepted Answer

A)  222.1 foot- pounds 
B)  53 foot- pounds 
C)  444.1 foot- pounds 
D)  85.4 foot- pounds 
A)  222.1 foot- pounds 
B)  53 foot- pounds 
C)  444.1 foot- pounds 
D)  85.4 foot- pounds

Question 19

A ssume all variables represent nonnegative real numbers.
-$\sqrt[5]{\mathrm{x}^{2} \mathrm{z}^{3}} \cdot \sqrt[5]{\mathrm{x}^{28} \mathrm{z}^{39}}$

Accepted Answer

A)  $x^{7} z^{8} \sqrt[5]{z}$ 
B)  $x^{6} z^{8} \sqrt[5]{z}$ 
C)  $x^{7} z^{9} \sqrt[5]{z^{2}}$ 
D)  $x^{6} z^{8} \sqrt[5]{z^{2}}$ 
A)  $x^{7} z^{8} \sqrt[5]{z}$ 
B)  $x^{6} z^{8} \sqrt[5]{z}$ 
C)  $x^{7} z^{9} \sqrt[5]{z^{2}}$ 
D)  $x^{6} z^{8} \sqrt[5]{z^{2}}$

Question 20

Simplify the expression. Assume all variables represent nonnegative real numbers.
-$\sqrt{5} \cdot \sqrt[5]{4}$

Accepted Answer

A)  $\sqrt[7]{50,000}$ 
B)  $\sqrt[10]{20}$ 
C)  $\sqrt[10]{50,000}$ 
D)  $\sqrt[10]{10,000}$ 
A)  $\sqrt[7]{50,000}$ 
B)  $\sqrt[10]{20}$ 
C)  $\sqrt[10]{50,000}$ 
D)  $\sqrt[10]{10,000}$

Add or subtract the complex numbers - $(4+8 \mathrm{i})-(-8+\mathrm{i})$

Simplify the expression. Assume all variables represent nonnegative real numbers. - $\left(b^{7 / 5}\right)^{5}$

Rewrite the radical expression using rational exponents. A ssume all variables represent nonnegative real numbers. - $\sqrt{\mathrm{x}^{9}}$

Multiply - $(3 \sqrt{2}+4 \sqrt{5})(4 \sqrt{11}-5 \sqrt{17})$

Multiply. - $4 \mathrm{i} \cdot \mathrm{-}$ 1i

Rationalize the denominator and simplify. A ssume all variables represent nonnegative real numbers. - $\sqrt{\frac{7}{27 \mathrm{xy}^{2}}}$

Find the domain of the function. Express the answer in interval notation. - $f(x)=\sqrt{2 x+2}$

A ssume all variables represent nonnegative real numbers. - $\sqrt{11}(\sqrt{11}-\sqrt{55})$

Use the Babylonian method to approximate the given square root to the nearest thousandth. - $\sqrt{600}$

Simplify the radical expression. If appropriate, include absolute values. - $\sqrt{196 y^{6}}$

Choose the one alternative that best completes the statement or answers thequestion. Express in terms of i. - $\sqrt{-81}$

Simplify the expression. Assume all variables represent nonnegative real numbers. - $z^{-2 / 7} \cdot z^{3 / 7}$

A student tries to solve $\sqrt{\mathrm{x}+7}=\sqrt{\mathrm{x}}+4$ by squaring both sides and gets $\mathrm{x}+7=\mathrm{x}+16$ . Why is this not correct?

Add or subtract the complex numbers - $(-7+2 \mathrm{i})-5$

Find the domain of the function. Express the answer in interval notation. - $f(x)=\sqrt[4]{x-19}$

Simplify. - $\frac{\sqrt{10}}{\sqrt{2}}$

$5 \sqrt[3]{3}-9 \sqrt{6}+2 \sqrt[3]{3}+7 \sqrt{6}$

A ssume all variables represent nonnegative real numbers. - $\sqrt[5]{\mathrm{x}^{2} \mathrm{z}^{3}} \cdot \sqrt[5]{\mathrm{x}^{28} \mathrm{z}^{39}}$

Simplify the expression. Assume all variables represent nonnegative real numbers. - $\sqrt{5} \cdot \sqrt[5]{4}$

Review of Real Numbers

Linear and Absolute Value Equations and Inequalities

Graphing Linear Equations

Systems of Equations

Exponents, Polynomials, and Factoring Polynomials

Rational Expressions and Equations

Quadratic Equations

Logarithmic and Exponential Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 7: Radical Expressions and Equations

Add or subtract the complex numbers - (4+8i)−(−8+i)(4+8 \mathrm{i})-(-8+\mathrm{i})(4+8i)−(−8+i)

Simplify the expression. Assume all variables represent nonnegative real numbers. - (b7/5)5\left(b^{7 / 5}\right)^{5}(b7/5)5

Rewrite the radical expression using rational exponents. A ssume all variables represent nonnegative real numbers. - x9\sqrt{\mathrm{x}^{9}}x9​

Multiply - (32+45)(411−517)(3 \sqrt{2}+4 \sqrt{5})(4 \sqrt{11}-5 \sqrt{17})(32​+45​)(411​−517​)

Multiply. - 4i⋅−4 \mathrm{i} \cdot \mathrm{-}4i⋅− 1i

Rationalize the denominator and simplify. A ssume all variables represent nonnegative real numbers. - 727xy2\sqrt{\frac{7}{27 \mathrm{xy}^{2}}}27xy27​​

Find the domain of the function. Express the answer in interval notation. - f(x)=2x+2f(x)=\sqrt{2 x+2}f(x)=2x+2​

A ssume all variables represent nonnegative real numbers. - 11(11−55)\sqrt{11}(\sqrt{11}-\sqrt{55})11​(11​−55​)

Use the Babylonian method to approximate the given square root to the nearest thousandth. - 600\sqrt{600}600​

Simplify the radical expression. If appropriate, include absolute values. - 196y6\sqrt{196 y^{6}}196y6​

Choose the one alternative that best completes the statement or answers thequestion. Express in terms of i. - −81\sqrt{-81}−81​

Simplify the expression. Assume all variables represent nonnegative real numbers. - z−2/7⋅z3/7z^{-2 / 7} \cdot z^{3 / 7}z−2/7⋅z3/7

A student tries to solve x+7=x+4\sqrt{\mathrm{x}+7}=\sqrt{\mathrm{x}}+4x+7​=x​+4 by squaring both sides and gets x+7=x+16\mathrm{x}+7=\mathrm{x}+16x+7=x+16 . Why is this not correct?

Add or subtract the complex numbers - (−7+2i)−5(-7+2 \mathrm{i})-5(−7+2i)−5

Find the domain of the function. Express the answer in interval notation. - f(x)=x−194f(x)=\sqrt[4]{x-19}f(x)=4x−19​

Simplify. - 102\frac{\sqrt{10}}{\sqrt{2}}2​10​​

533−96+233+765 \sqrt[3]{3}-9 \sqrt{6}+2 \sqrt[3]{3}+7 \sqrt{6}533​−96​+233​+76​

A ssume all variables represent nonnegative real numbers. - x2z35⋅x28z395\sqrt[5]{\mathrm{x}^{2} \mathrm{z}^{3}} \cdot \sqrt[5]{\mathrm{x}^{28} \mathrm{z}^{39}}5x2z3​⋅5x28z39​

Simplify the expression. Assume all variables represent nonnegative real numbers. - 5⋅45\sqrt{5} \cdot \sqrt[5]{4}5​⋅54​

Review of Real Numbers

Linear and Absolute Value Equations and Inequalities

Graphing Linear Equations

Systems of Equations

Exponents, Polynomials, and Factoring Polynomials

Rational Expressions and Equations

Quadratic Equations

Logarithmic and Exponential Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Add or subtract the complex numbers - $(4+8 \mathrm{i})-(-8+\mathrm{i})$

Simplify the expression. Assume all variables represent nonnegative real numbers. - $\left(b^{7 / 5}\right)^{5}$

Rewrite the radical expression using rational exponents. A ssume all variables represent nonnegative real numbers. - $\sqrt{\mathrm{x}^{9}}$

Multiply - $(3 \sqrt{2}+4 \sqrt{5})(4 \sqrt{11}-5 \sqrt{17})$

Multiply. - $4 \mathrm{i} \cdot \mathrm{-}$ 1i

Rationalize the denominator and simplify. A ssume all variables represent nonnegative real numbers. - $\sqrt{\frac{7}{27 \mathrm{xy}^{2}}}$

Find the domain of the function. Express the answer in interval notation. - $f(x)=\sqrt{2 x+2}$

A ssume all variables represent nonnegative real numbers. - $\sqrt{11}(\sqrt{11}-\sqrt{55})$

Use the Babylonian method to approximate the given square root to the nearest thousandth. - $\sqrt{600}$

Simplify the radical expression. If appropriate, include absolute values. - $\sqrt{196 y^{6}}$

Choose the one alternative that best completes the statement or answers thequestion. Express in terms of i. - $\sqrt{-81}$

Simplify the expression. Assume all variables represent nonnegative real numbers. - $z^{-2 / 7} \cdot z^{3 / 7}$

A student tries to solve $\sqrt{\mathrm{x}+7}=\sqrt{\mathrm{x}}+4$ by squaring both sides and gets $\mathrm{x}+7=\mathrm{x}+16$ . Why is this not correct?

Add or subtract the complex numbers - $(-7+2 \mathrm{i})-5$

Find the domain of the function. Express the answer in interval notation. - $f(x)=\sqrt[4]{x-19}$

Simplify. - $\frac{\sqrt{10}}{\sqrt{2}}$

$5 \sqrt[3]{3}-9 \sqrt{6}+2 \sqrt[3]{3}+7 \sqrt{6}$

A ssume all variables represent nonnegative real numbers. - $\sqrt[5]{\mathrm{x}^{2} \mathrm{z}^{3}} \cdot \sqrt[5]{\mathrm{x}^{28} \mathrm{z}^{39}}$

Simplify the expression. Assume all variables represent nonnegative real numbers. - $\sqrt{5} \cdot \sqrt[5]{4}$