Question 1

Simplify the radical expression. Assume all variables represent nonnegative real numbers.
-$\sqrt{m^{7} n^{8}}$

Accepted Answer

A)  $m^{3} n^{4} \sqrt{m}$ 
B)  $m^{3} n^{4}$ 
C)  $m^{4} n^{5}$ 
D)  $m^{3} n^{8} \sqrt{m}$ 
A)  $m^{3} n^{4} \sqrt{m}$ 
B)  $m^{3} n^{4}$ 
C)  $m^{4} n^{5}$ 
D)  $m^{3} n^{8} \sqrt{m}$

Question 2

Rationalize the denominator and simplify. A ssume all variables represent nonnegative real numbers.
-$\frac{7}{\sqrt{5}}$

Accepted Answer

A)  $\frac{7 \sqrt{5}}{5}$ 
B)  $\frac{49 \sqrt{5}}{5}$ 
C)  $7 \sqrt{5}$ 
D)  32 
A)  $\frac{7 \sqrt{5}}{5}$ 
B)  $\frac{49 \sqrt{5}}{5}$ 
C)  $7 \sqrt{5}$ 
D)  32

Question 3

Simplify. Assume all variables represent nonnegative values.
-$\frac{\sqrt{25 y}}{\sqrt{5 y}}$

Accepted Answer

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

Question 4

Simplify the radical expression. Assume all variables represent nonnegative real numbers.
-$-\sqrt[3]{-64 \mathrm{x}^{3}}$

Accepted Answer

A)  $-4 x$ 
B)  $4 x$ 
C)  $4 x^{3}$ 
D)  $-64 x$ 
A)  $-4 x$ 
B)  $4 x$ 
C)  $4 x^{3}$ 
D)  $-64 x$

Question 5

If a pendulum has a period of 1.7 seconds, find its length in inches. Use the formula $T=2 \pi \sqrt{\frac{L}{384}}$.

Accepted Answer

A)  $56.22 \mathrm{in}$. 
B)  $28.11 \mathrm{in}$. 
C)  $14.06 \mathrm{in}$. 
D)  $0.42 \mathrm{in}$. 
A)  $56.22 \mathrm{in}$. 
B)  $28.11 \mathrm{in}$. 
C)  $14.06 \mathrm{in}$. 
D)  $0.42 \mathrm{in}$.

Question 6

Simplify.
-$\sqrt{8} \cdot \sqrt{2}$

Accepted Answer

A)  $2 \sqrt{4}$ 
B)  16 
C)  4 
D)  $2 \sqrt{2}$ 
A)  $2 \sqrt{4}$ 
B)  16 
C)  4 
D)  $2 \sqrt{2}$

Question 7

Explain why the equation $x^{2}=16$ has two real- number solutions, while the equation $\sqrt{\mathrm{x}}=4$ has only one real number solution.

Accepted Answer

Answers may vary. One possibility: Takin

Question 8

Find the missing complex number
-$(7+4 \mathrm{i})-?=13+3 \mathrm{i}$

Accepted Answer

A)  $-6-i$ 
B)  $-6+i$ 
C)  $-13-3 i$ 
D)  $13-3 \mathrm{i}$ 
A)  $-6-i$ 
B)  $-6+i$ 
C)  $-13-3 i$ 
D)  $13-3 \mathrm{i}$

Question 9

Multiply the conjugates.
-$(\sqrt{10}+1)(\sqrt{10}-1)$

Accepted Answer

A)  11 
B)  $9-2 \sqrt{10}$ 
C)  $9+2 \sqrt{10}$ 
D)  9 
A)  11 
B)  $9-2 \sqrt{10}$ 
C)  $9+2 \sqrt{10}$ 
D)  9

Question 10

Rewrite the radical expression using rational exponents. A ssume all variables represent nonnegative real numbers.
-$\sqrt[8]{m^{7}}$

Accepted Answer

A)  $m^{7 / 8}$ 
B)  $\frac{1}{(m n)^{8}}$ 
C)  $-m^{7 / 8}$ 
D)  $m^{8 / 7}$ 
A)  $m^{7 / 8}$ 
B)  $\frac{1}{(m n)^{8}}$ 
C)  $-m^{7 / 8}$ 
D)  $m^{8 / 7}$

Question 11

For the function $f(x)=\sqrt{x-3}$, find all values $x$ for which $f(x)=4$.

Accepted Answer

A)  7 
B)  13 
C)  49 
D)  19 
A)  7 
B)  13 
C)  49 
D)  19

Question 12

Simplify.
-$\frac{\sqrt{729}}{\sqrt{9}}$

Accepted Answer

A)  3 
B)  81 
C)  9 
D)  27 
A)  3 
B)  81 
C)  9 
D)  27

Question 13

$7 \div(-3+6 i)$

Accepted Answer

A)  $\frac{7}{9}-\frac{14}{9} \mathrm{i}$ 
B)  $-\frac{7}{15}+\frac{14}{15} \mathrm{i}$ 
C)  $\frac{7}{9}+\frac{14}{9} \mathrm{i}$ 
D)  $-\frac{7}{15}-\frac{14}{15} \mathrm{i}$ 
A)  $\frac{7}{9}-\frac{14}{9} \mathrm{i}$ 
B)  $-\frac{7}{15}+\frac{14}{15} \mathrm{i}$ 
C)  $\frac{7}{9}+\frac{14}{9} \mathrm{i}$ 
D)  $-\frac{7}{15}-\frac{14}{15} \mathrm{i}$

Question 14

A manufacturer's cost is given by $C=100 \sqrt[3]{n}+200$, where $C$ is the cost and $n$ is the number of parts produced. Find the cost when 512 parts are produced.

Accepted Answer

A)  $\$ 2463$ 
B)  $\$ 1000$ 
C)  $\$ 13$ 
D)  $\$ 600$ 
A)  $\$ 2463$ 
B)  $\$ 1000$ 
C)  $\$ 13$ 
D)  $\$ 600$

Question 15

Multiply. Write your answer in a +bi form.
-$(3-7 i)(9-8 i)$

Accepted Answer

A)  $-29+87 i$ 
B)  $83-39 \mathrm{i}$ 
C)  $56 \mathrm{i}^{2}-87 \mathrm{i}+27$ 
D)  - 29- $87 \mathrm{i}$ 
A)  $-29+87 i$ 
B)  $83-39 \mathrm{i}$ 
C)  $56 \mathrm{i}^{2}-87 \mathrm{i}+27$ 
D)  - 29- $87 \mathrm{i}$

Question 16

Simplify the expression. Assume all variables represent nonnegative real numbers.
-$\sqrt{3} \cdot \sqrt[3]{4}$

Accepted Answer

A)  $\sqrt[6]{108}$ 
B)  $\sqrt[6]{12}$ 
C)  $\sqrt[6]{144}$ 
D)  $\sqrt[6]{432}$ 
A)  $\sqrt[6]{108}$ 
B)  $\sqrt[6]{12}$ 
C)  $\sqrt[6]{144}$ 
D)  $\sqrt[6]{432}$

Question 17

Find the missing complex number
-$(6-9 \mathrm{i})(?)=7+2 \mathrm{i}$

Accepted Answer

A)  $-\frac{4}{3}+\frac{5}{9} \mathrm{i}$ 
B)  $-\frac{8}{45}+\frac{5}{9} \mathrm{i}$ 
C)  $\frac{20}{13}+\frac{17}{13} \mathrm{i}$ 
D)  $\frac{8}{39}+\frac{25}{39} \mathrm{i}$ 
A)  $-\frac{4}{3}+\frac{5}{9} \mathrm{i}$ 
B)  $-\frac{8}{45}+\frac{5}{9} \mathrm{i}$ 
C)  $\frac{20}{13}+\frac{17}{13} \mathrm{i}$ 
D)  $\frac{8}{39}+\frac{25}{39} \mathrm{i}$

Question 18

Solve. Check for extraneous solutions.
-$x=\sqrt{x+13}+7$

Accepted Answer

A)  $\{12\}$ 
B)  $\{-9\}$ 
C)  $\{3\}$ 
D)  $\{3,12\}$ 
A)  $\{12\}$ 
B)  $\{-9\}$ 
C)  $\{3\}$ 
D)  $\{3,12\}$

Question 19

$\mathrm{i} ^{33} \cdot \mathrm{i} ^{31}$

Accepted Answer

A)  - 1 
B)  1 
C)  i 
D)  - i 
A)  - 1 
B)  1 
C)  i 
D)  - i

Question 20

Rationalize the denominator and simplify.
-$\frac{3 \sqrt{3}+\sqrt{11}}{5 \sqrt{3}+\sqrt{13}}$

Accepted Answer

A)  $\frac{45+2 \sqrt{6}-\sqrt{143}}{62}$ 
B)  $\frac{45+5 \sqrt{33}-3 \sqrt{39}-\sqrt{143}}{88}$ 
C)  $\frac{45+5 \sqrt{33}+3 \sqrt{39}+\sqrt{143}}{62}$ 
D)  $\frac{45+5 \sqrt{33}-3 \sqrt{39}-\sqrt{143}}{62}$ 
A)  $\frac{45+2 \sqrt{6}-\sqrt{143}}{62}$ 
B)  $\frac{45+5 \sqrt{33}-3 \sqrt{39}-\sqrt{143}}{88}$ 
C)  $\frac{45+5 \sqrt{33}+3 \sqrt{39}+\sqrt{143}}{62}$ 
D)  $\frac{45+5 \sqrt{33}-3 \sqrt{39}-\sqrt{143}}{62}$

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - $\sqrt{m^{7} n^{8}}$

Rationalize the denominator and simplify. A ssume all variables represent nonnegative real numbers. - $\frac{7}{\sqrt{5}}$

Simplify. Assume all variables represent nonnegative values. - $\frac{\sqrt{25 y}}{\sqrt{5 y}}$

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - $-\sqrt[3]{-64 \mathrm{x}^{3}}$

If a pendulum has a period of 1.7 seconds, find its length in inches. Use the formula $T=2 \pi \sqrt{\frac{L}{384}}$ .

Simplify. - $\sqrt{8} \cdot \sqrt{2}$

Explain why the equation $x^{2}=16$ has two real- number solutions, while the equation $\sqrt{\mathrm{x}}=4$ has only one real number solution.

Find the missing complex number - $(7+4 \mathrm{i})-?=13+3 \mathrm{i}$

Multiply the conjugates. - $(\sqrt{10}+1)(\sqrt{10}-1)$

Rewrite the radical expression using rational exponents. A ssume all variables represent nonnegative real numbers. - $\sqrt[8]{m^{7}}$

For the function $f(x)=\sqrt{x-3}$ , find all values $x$ for which $f(x)=4$ .

Simplify. - $\frac{\sqrt{729}}{\sqrt{9}}$

$7 \div(-3+6 i)$

A manufacturer's cost is given by $C=100 \sqrt[3]{n}+200$ , where $C$ is the cost and $n$ is the number of parts produced. Find the cost when 512 parts are produced.

Multiply. Write your answer in a +bi form. - $(3-7 i)(9-8 i)$

Simplify the expression. Assume all variables represent nonnegative real numbers. - $\sqrt{3} \cdot \sqrt[3]{4}$

Find the missing complex number - $(6-9 \mathrm{i})(?)=7+2 \mathrm{i}$

Solve. Check for extraneous solutions. - $x=\sqrt{x+13}+7$

$\mathrm{i} ^{33} \cdot \mathrm{i} ^{31}$

Rationalize the denominator and simplify. - $\frac{3 \sqrt{3}+\sqrt{11}}{5 \sqrt{3}+\sqrt{13}}$

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

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - m7n8\sqrt{m^{7} n^{8}}m7n8​

Rationalize the denominator and simplify. A ssume all variables represent nonnegative real numbers. - 75\frac{7}{\sqrt{5}}5​7​

Simplify. Assume all variables represent nonnegative values. - 25y5y\frac{\sqrt{25 y}}{\sqrt{5 y}}5y​25y​​

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - −−64x33-\sqrt[3]{-64 \mathrm{x}^{3}}−3−64x3​

If a pendulum has a period of 1.7 seconds, find its length in inches. Use the formula T=2πL384T=2 \pi \sqrt{\frac{L}{384}}T=2π384L​​ .

Simplify. - 8⋅2\sqrt{8} \cdot \sqrt{2}8​⋅2​

Explain why the equation x2=16x^{2}=16x2=16 has two real- number solutions, while the equation x=4\sqrt{\mathrm{x}}=4x​=4 has only one real number solution.

Find the missing complex number - (7+4i)−?=13+3i(7+4 \mathrm{i})-?=13+3 \mathrm{i}(7+4i)−?=13+3i

Multiply the conjugates. - (10+1)(10−1)(\sqrt{10}+1)(\sqrt{10}-1)(10​+1)(10​−1)

Rewrite the radical expression using rational exponents. A ssume all variables represent nonnegative real numbers. - m78\sqrt[8]{m^{7}}8m7​

For the function f(x)=x−3f(x)=\sqrt{x-3}f(x)=x−3​ , find all values xxx for which f(x)=4f(x)=4f(x)=4 .

Simplify. - 7299\frac{\sqrt{729}}{\sqrt{9}}9​729​​

7÷(−3+6i)7 \div(-3+6 i)7÷(−3+6i)

A manufacturer's cost is given by C=100n3+200C=100 \sqrt[3]{n}+200C=1003n​+200 , where CCC is the cost and nnn is the number of parts produced. Find the cost when 512 parts are produced.

Multiply. Write your answer in a +bi form. - (3−7i)(9−8i)(3-7 i)(9-8 i)(3−7i)(9−8i)

Simplify the expression. Assume all variables represent nonnegative real numbers. - 3⋅43\sqrt{3} \cdot \sqrt[3]{4}3​⋅34​

Find the missing complex number - (6−9i)(?)=7+2i(6-9 \mathrm{i})(?)=7+2 \mathrm{i}(6−9i)(?)=7+2i

Solve. Check for extraneous solutions. - x=x+13+7x=\sqrt{x+13}+7x=x+13​+7

i33⋅i31\mathrm{i} ^{33} \cdot \mathrm{i} ^{31}i33⋅i31

Rationalize the denominator and simplify. - 33+1153+13\frac{3 \sqrt{3}+\sqrt{11}}{5 \sqrt{3}+\sqrt{13}}53​+13​33​+11​​

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

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - $\sqrt{m^{7} n^{8}}$

Rationalize the denominator and simplify. A ssume all variables represent nonnegative real numbers. - $\frac{7}{\sqrt{5}}$

Simplify. Assume all variables represent nonnegative values. - $\frac{\sqrt{25 y}}{\sqrt{5 y}}$

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - $-\sqrt[3]{-64 \mathrm{x}^{3}}$

If a pendulum has a period of 1.7 seconds, find its length in inches. Use the formula $T=2 \pi \sqrt{\frac{L}{384}}$ .

Simplify. - $\sqrt{8} \cdot \sqrt{2}$

Explain why the equation $x^{2}=16$ has two real- number solutions, while the equation $\sqrt{\mathrm{x}}=4$ has only one real number solution.

Find the missing complex number - $(7+4 \mathrm{i})-?=13+3 \mathrm{i}$

Multiply the conjugates. - $(\sqrt{10}+1)(\sqrt{10}-1)$

Rewrite the radical expression using rational exponents. A ssume all variables represent nonnegative real numbers. - $\sqrt[8]{m^{7}}$

For the function $f(x)=\sqrt{x-3}$ , find all values $x$ for which $f(x)=4$ .

Simplify. - $\frac{\sqrt{729}}{\sqrt{9}}$

$7 \div(-3+6 i)$

A manufacturer's cost is given by $C=100 \sqrt[3]{n}+200$ , where $C$ is the cost and $n$ is the number of parts produced. Find the cost when 512 parts are produced.

Multiply. Write your answer in a +bi form. - $(3-7 i)(9-8 i)$

Simplify the expression. Assume all variables represent nonnegative real numbers. - $\sqrt{3} \cdot \sqrt[3]{4}$

Find the missing complex number - $(6-9 \mathrm{i})(?)=7+2 \mathrm{i}$

Solve. Check for extraneous solutions. - $x=\sqrt{x+13}+7$

$\mathrm{i} ^{33} \cdot \mathrm{i} ^{31}$

Rationalize the denominator and simplify. - $\frac{3 \sqrt{3}+\sqrt{11}}{5 \sqrt{3}+\sqrt{13}}$