Question 1

Find the missing complex number
-$\frac{?}{8+2 \mathrm{i}}=2-6 \mathrm{i}$

Accepted Answer

A)  $28-44 \mathrm{i}$ 
B)  $4+52 \mathrm{i}$ 
C)  $28+44 \mathrm{i}$ 
D)  $-12 i^{2}-44 i+16$ 
A)  $28-44 \mathrm{i}$ 
B)  $4+52 \mathrm{i}$ 
C)  $28+44 \mathrm{i}$ 
D)  $-12 i^{2}-44 i+16$

Question 2

Solve. Check for extraneous solutions.
-$(x+4)^{1 / 3}=4$

Accepted Answer

A)  $\{0\}$ 
B)  $\{60\}$ 
C)  $\{64\}$ 
D)  $\{12\}$ 
A)  $\{0\}$ 
B)  $\{60\}$ 
C)  $\{64\}$ 
D)  $\{12\}$

Question 3

Simplify the radical expression. If appropriate, include absolute values.
-$\sqrt{4 x^{2}+24 x+36}$

Accepted Answer

A)  $|2 x+6|$ 
B)  $2 x+6+\sqrt{24 x}$ 
C)  $|2 x-6|$ 
D)  $-2 x+8$ 
A)  $|2 x+6|$ 
B)  $2 x+6+\sqrt{24 x}$ 
C)  $|2 x-6|$ 
D)  $-2 x+8$

Question 4

A ssume all variables represent nonnegative real numbers.
-$\sqrt{2}(8+\sqrt{2})$

Accepted Answer

A)  $9 \sqrt{2}$ 
B)  $8 \sqrt{2}+2$ 
C)  $8 \sqrt{2}-2$ 
D)  $2 \sqrt{2}+8$ 
A)  $9 \sqrt{2}$ 
B)  $8 \sqrt{2}+2$ 
C)  $8 \sqrt{2}-2$ 
D)  $2 \sqrt{2}+8$

Question 5

olve. Check for extraneous solutions.
-$\sqrt[3]{\mathrm{x}+6}=5$

Accepted Answer

A)  $\{-1\}$ 
B)  $\{119\}$ 
C)  $\{19\}$ 
D)  $\{125\}$ 
A)  $\{-1\}$ 
B)  $\{119\}$ 
C)  $\{19\}$ 
D)  $\{125\}$

Question 6

Find the missing complex number
-$(6+6 \mathrm{i})-?=10+5 \mathrm{i}$

Accepted Answer

A)  -4 - i 
B)  $-4+i$ 
C)  $-10-5 i$ 
D)  $10-5 \mathrm{i}$ 
A)  -4 - i 
B)  $-4+i$ 
C)  $-10-5 i$ 
D)  $10-5 \mathrm{i}$

Question 7

A ssume all variables represent nonnegative real numbers.
-$\sqrt[3]{\mathrm{x}}\left(\sqrt[3]{\mathrm{x}^{2}}-\sqrt[3]{81 \mathrm{x}^{2}}\right)$

Accepted Answer

A)  $x-3 x^{3} \sqrt[3]{3}$ 
B)  $x-3 x \sqrt[3]{3}$ 
C)  $x-9 x$ 
D)  $x-27 x \sqrt[3]{3}$ 
A)  $x-3 x^{3} \sqrt[3]{3}$ 
B)  $x-3 x \sqrt[3]{3}$ 
C)  $x-9 x$ 
D)  $x-27 x \sqrt[3]{3}$

Question 8

The radius, $r$, of a sphere can be found using the formula $r=\sqrt{\frac{S}{4 \pi}}$, where $S$ is the surface area. If the surface area is 15,253 square inches, what is the radius? (Use 3.14 for $\pi$, and round your answer to the nearest tenth of an inch.)

Accepted Answer

A)  34.8 in. 
B)  $69.6 \mathrm{in}$. 
C)  $61.8 \mathrm{in.}$ 
D)  $109.4 \mathrm{in}$. 
A)  34.8 in. 
B)  $69.6 \mathrm{in}$. 
C)  $61.8 \mathrm{in.}$ 
D)  $109.4 \mathrm{in}$.

Question 9

Rewrite the radical expression using rational exponents. A ssume all variables represent nonnegative real numbers.
-$\left(\sqrt[5]{5 x^{3} y}\right)^{2}$

Accepted Answer

A)  $(5 x y)^{6 / 5}$ 
B)  $\left(5 x^{3} y\right)^{5 / 2}$ 
C)  $\left(5 x^{3} y\right)^{2 / 5}$ 
D)  $\left(5 x^{3} y\right)^{10}$ 
A)  $(5 x y)^{6 / 5}$ 
B)  $\left(5 x^{3} y\right)^{5 / 2}$ 
C)  $\left(5 x^{3} y\right)^{2 / 5}$ 
D)  $\left(5 x^{3} y\right)^{10}$

Question 10

Tell whether the statement is true or false. If it is false, give the correct answer. Explain your answer. The easiest way to simplify the expression $\frac{10}{4+\sqrt{8}}$ is to multiply both the numerator and denominator by $4+\sqrt{8}$.

Accepted Answer

The statement is false. The easiest way

Question 11

Simplify the radical expression. Assume all variables represent nonnegative real numbers.
-$\sqrt[3]{216}$

Accepted Answer

A)  15 
B)  -6 
C)  36 
D)  6 
A)  15 
B)  -6 
C)  36 
D)  6

Question 12

Simplify by rationalizing the denominator. Write your answer in a + bi form.
-$\frac{-7}{-4-5 i}$

Accepted Answer

A)  $\frac{28}{41}+\frac{35}{41} \mathrm{i}$ 
B)  $-\frac{28}{9}+\frac{35}{9} \mathrm{i}$ 
C)  $\frac{28}{41}-\frac{35}{41} \mathrm{i}$ 
D)  $-\frac{28}{9}-\frac{35}{9} \mathrm{i}$ 
A)  $\frac{28}{41}+\frac{35}{41} \mathrm{i}$ 
B)  $-\frac{28}{9}+\frac{35}{9} \mathrm{i}$ 
C)  $\frac{28}{41}-\frac{35}{41} \mathrm{i}$ 
D)  $-\frac{28}{9}-\frac{35}{9} \mathrm{i}$

Question 13

Solve. Check for extraneous solutions.
-$\sqrt{3 \mathrm{x}+1}=3+\sqrt{\mathrm{x}-4}$

Accepted Answer

A)  $\{-1\}$ 
B)  $\{5,8\}$ 
C)  $\{-5,-8\}$ 
D)  $\varnothing$ 
A)  $\{-1\}$ 
B)  $\{5,8\}$ 
C)  $\{-5,-8\}$ 
D)  $\varnothing$

Question 14

Find the missing complex number
-$(7+\mathrm{i})(?)=55+15 \mathrm{i}$

Accepted Answer

A)  $\frac{7}{48}+\frac{1}{48} \mathrm{i}$ 
B)  $\frac{4}{25}+\frac{3}{10} \mathrm{i}$ 
C)  7 - 1 
D)  $8+i$ 
A)  $\frac{7}{48}+\frac{1}{48} \mathrm{i}$ 
B)  $\frac{4}{25}+\frac{3}{10} \mathrm{i}$ 
C)  7 - 1 
D)  $8+i$

Question 15

olve. Check for extraneous solutions.
-$\sqrt[4]{\mathrm{x}+5}+7=0$

Accepted Answer

A)  $\left\{\frac{2401}{5}\right\}$ 
B)  $\left\{\frac{7}{5}\right\}$ 
C)  $\left\{-\frac{2401}{5}\right\}$ 
D)  $\varnothing$ 
A)  $\left\{\frac{2401}{5}\right\}$ 
B)  $\left\{\frac{7}{5}\right\}$ 
C)  $\left\{-\frac{2401}{5}\right\}$ 
D)  $\varnothing$

Question 16

On a test track with the given drag factor, a test driver hit the brakes once the car had reached the given speed. Use the formula $s=\sqrt{30 \mathrm{df}}$ to find the length of the skid marks the car made if it was traveling at $50 \mathrm{mph}$ on concrete ( $\mathrm{f}=0.95)$. Round to the nearest foot if necessary.

Accepted Answer

A)  83 feet 
B)  81 feet 
C)  88 feet 
D)  85 feet 
A)  83 feet 
B)  81 feet 
C)  88 feet 
D)  85 feet

Question 17

The radius of a sphere depends on its surface area, $S$, and is given by the formula
$r=\sqrt{\frac{\mathrm{S}}{4 \pi}}$.
What is the surface area of a sphere with radius of 8.8 inches?
Use 3.14 for $\pi$. Round to the nearest tenth of a square inch.

Accepted Answer

A)  110.5 square inches 
B)  972.6 square inches 
C)  243.2 square inches 
D)  27.6 square inches 
A)  110.5 square inches 
B)  972.6 square inches 
C)  243.2 square inches 
D)  27.6 square inches

Question 18

Simplify the radical expression. If appropriate, include absolute values.
-$\sqrt{z^{2}-20 z+100}$

Accepted Answer

A)  $-z+10$ 
B)  $z-10 \mid$ 
C)  $\mathrm{z}-10$ 
D)  $|z|-10$ 
A)  $-z+10$ 
B)  $z-10 \mid$ 
C)  $\mathrm{z}-10$ 
D)  $|z|-10$

Question 19

Rationalize the denominator and simplify. A ssume all variables represent nonnegative real numbers.
-$\frac{11}{\sqrt{11}}$

Accepted Answer

A)  $\sqrt{11}$ 
B)  1 
C)  $11 \sqrt{11}$ 
D)  11 
A)  $\sqrt{11}$ 
B)  1 
C)  $11 \sqrt{11}$ 
D)  11

Question 20

Multiply. Write your answer in a +bi form.
-$(1-4 \mathrm{i})^{2}$

Accepted Answer

A)  $17-8 \mathrm{i}$ 
B)  $1+8 \mathrm{i}$ 
C)  1 - 24i 
D)  $-15-8 \mathrm{i}$ 
A)  $17-8 \mathrm{i}$ 
B)  $1+8 \mathrm{i}$ 
C)  1 - 24i 
D)  $-15-8 \mathrm{i}$

Find the missing complex number - $\frac{?}{8+2 \mathrm{i}}=2-6 \mathrm{i}$

Solve. Check for extraneous solutions. - $(x+4)^{1 / 3}=4$

Simplify the radical expression. If appropriate, include absolute values. - $\sqrt{4 x^{2}+24 x+36}$

A ssume all variables represent nonnegative real numbers. - $\sqrt{2}(8+\sqrt{2})$

olve. Check for extraneous solutions. - $\sqrt[3]{\mathrm{x}+6}=5$

Find the missing complex number - $(6+6 \mathrm{i})-?=10+5 \mathrm{i}$

A ssume all variables represent nonnegative real numbers. - $\sqrt[3]{\mathrm{x}}\left(\sqrt[3]{\mathrm{x}^{2}}-\sqrt[3]{81 \mathrm{x}^{2}}\right)$

The radius, $r$ , of a sphere can be found using the formula $r=\sqrt{\frac{S}{4 \pi}}$ , where $S$ is the surface area. If the surface area is 15,253 square inches, what is the radius? (Use 3.14 for $\pi$ , and round your answer to the nearest tenth of an inch.)

Rewrite the radical expression using rational exponents. A ssume all variables represent nonnegative real numbers. - $\left(\sqrt[5]{5 x^{3} y}\right)^{2}$

Tell whether the statement is true or false. If it is false, give the correct answer. Explain your answer. The easiest way to simplify the expression $\frac{10}{4+\sqrt{8}}$ is to multiply both the numerator and denominator by $4+\sqrt{8}$ .

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - $\sqrt[3]{216}$

Simplify by rationalizing the denominator. Write your answer in a + bi form. - $\frac{-7}{-4-5 i}$

Solve. Check for extraneous solutions. - $\sqrt{3 \mathrm{x}+1}=3+\sqrt{\mathrm{x}-4}$

Find the missing complex number - $(7+\mathrm{i})(?)=55+15 \mathrm{i}$

olve. Check for extraneous solutions. - $\sqrt[4]{\mathrm{x}+5}+7=0$

The radius of a sphere depends on its surface area, $S$ , and is given by the formula $r=\sqrt{\frac{\mathrm{S}}{4 \pi}}$ . What is the surface area of a sphere with radius of 8.8 inches? Use 3.14 for $\pi$ . Round to the nearest tenth of a square inch.

Simplify the radical expression. If appropriate, include absolute values. - $\sqrt{z^{2}-20 z+100}$

Rationalize the denominator and simplify. A ssume all variables represent nonnegative real numbers. - $\frac{11}{\sqrt{11}}$

Multiply. Write your answer in a +bi form. - $(1-4 \mathrm{i})^{2}$

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

Find the missing complex number - ?8+2i=2−6i\frac{?}{8+2 \mathrm{i}}=2-6 \mathrm{i}8+2i?​=2−6i

Solve. Check for extraneous solutions. - (x+4)1/3=4(x+4)^{1 / 3}=4(x+4)1/3=4

Simplify the radical expression. If appropriate, include absolute values. - 4x2+24x+36\sqrt{4 x^{2}+24 x+36}4x2+24x+36​

A ssume all variables represent nonnegative real numbers. - 2(8+2)\sqrt{2}(8+\sqrt{2})2​(8+2​)

olve. Check for extraneous solutions. - x+63=5\sqrt[3]{\mathrm{x}+6}=53x+6​=5

Find the missing complex number - (6+6i)−?=10+5i(6+6 \mathrm{i})-?=10+5 \mathrm{i}(6+6i)−?=10+5i

A ssume all variables represent nonnegative real numbers. - x3(x23−81x23)\sqrt[3]{\mathrm{x}}\left(\sqrt[3]{\mathrm{x}^{2}}-\sqrt[3]{81 \mathrm{x}^{2}}\right)3x​(3x2​−381x2​)

The radius, rrr , of a sphere can be found using the formula r=S4πr=\sqrt{\frac{S}{4 \pi}}r=4πS​​ , where SSS is the surface area. If the surface area is 15,253 square inches, what is the radius? (Use 3.14 for π\piπ , and round your answer to the nearest tenth of an inch.)

Rewrite the radical expression using rational exponents. A ssume all variables represent nonnegative real numbers. - (5x3y5)2\left(\sqrt[5]{5 x^{3} y}\right)^{2}(55x3y​)2

Tell whether the statement is true or false. If it is false, give the correct answer. Explain your answer. The easiest way to simplify the expression 104+8\frac{10}{4+\sqrt{8}}4+8​10​ is to multiply both the numerator and denominator by 4+84+\sqrt{8}4+8​ .

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - 2163\sqrt[3]{216}3216​

Simplify by rationalizing the denominator. Write your answer in a + bi form. - −7−4−5i\frac{-7}{-4-5 i}−4−5i−7​

Solve. Check for extraneous solutions. - 3x+1=3+x−4\sqrt{3 \mathrm{x}+1}=3+\sqrt{\mathrm{x}-4}3x+1​=3+x−4​

Find the missing complex number - (7+i)(?)=55+15i(7+\mathrm{i})(?)=55+15 \mathrm{i}(7+i)(?)=55+15i

olve. Check for extraneous solutions. - x+54+7=0\sqrt[4]{\mathrm{x}+5}+7=04x+5​+7=0

The radius of a sphere depends on its surface area, SSS , and is given by the formula r=S4πr=\sqrt{\frac{\mathrm{S}}{4 \pi}}r=4πS​​ . What is the surface area of a sphere with radius of 8.8 inches? Use 3.14 for π\piπ . Round to the nearest tenth of a square inch.

Simplify the radical expression. If appropriate, include absolute values. - z2−20z+100\sqrt{z^{2}-20 z+100}z2−20z+100​

Rationalize the denominator and simplify. A ssume all variables represent nonnegative real numbers. - 1111\frac{11}{\sqrt{11}}11​11​

Multiply. Write your answer in a +bi form. - (1−4i)2(1-4 \mathrm{i})^{2}(1−4i)2