Question 1

Multiply. Write your answer in a +bi form.
-$4 \mathrm{i}(8-9 \mathrm{i})$

Accepted Answer

A)  $32 i-36 i^{2}$ 
B)  $36+32 \mathrm{i}$ 
C)  $32 \mathrm{i}-36$ 
D)  $32 i+36 i^{2}$ 
A)  $32 i-36 i^{2}$ 
B)  $36+32 \mathrm{i}$ 
C)  $32 \mathrm{i}-36$ 
D)  $32 i+36 i^{2}$

Question 2

The rms velocity (or average velocity) of a gas particle in meters per second is given by the formula $\mu_{\mathrm{rms}}=\sqrt{\frac{24.9435 \mathrm{~T}}{\mathrm{M}}}$, where $\mathrm{T}$ is the absolute temperature in kelvin $\left(\mathrm{T}=\mathrm{T}_{\mathrm{C}}+273\right)$ and $\mathrm{M}$ is the molar mass (mass of 1 mole) of the gas in kilograms. Find the rms velocity for a molecule of Hydrogen $\left(\mathrm{H}_{2}\right)$ with molar mass 0.002 kilogram at a temperature of $70^{\circ} \mathrm{C}$. Round to the nearest tenth of a meter per second.

Accepted Answer

A)  $414.1 \mathrm{~m} / \mathrm{s}$ 
B)  $2068.3 \mathrm{~m} / \mathrm{s}$ 
C)  $1759.9 \mathrm{~m} / \mathrm{s}$ 
D)  $934.4 \mathrm{~m} / \mathrm{s}$ 
A)  $414.1 \mathrm{~m} / \mathrm{s}$ 
B)  $2068.3 \mathrm{~m} / \mathrm{s}$ 
C)  $1759.9 \mathrm{~m} / \mathrm{s}$ 
D)  $934.4 \mathrm{~m} / \mathrm{s}$

Question 3

$\frac{\mathrm{i}^{40}}{\mathrm{i}^{38}}$

Accepted Answer

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

Question 4

Choose values for $n$, a, and $b$ to demonstrate the truth or falsity of the statement:
$$\sqrt[n]{\mathrm{a}}+\sqrt[n]{\mathrm{b}}=\sqrt[n]{\mathrm{a}+\mathrm{b}}$$

Accepted Answer

A) True 
 B)False

Question 5

Rationalize the denominator and simplify.
-$\frac{3-\sqrt{10}}{3+\sqrt{10}}$

Accepted Answer

A)  $\frac{19+6 \sqrt{10}}{-1}$ 
B)  $\frac{-1-6 \sqrt{10}}{19}$ 
C)  $\frac{-1+6 \sqrt{10}}{19}$ 
D)  $\frac{19-6 \sqrt{10}}{-1}$ 
A)  $\frac{19+6 \sqrt{10}}{-1}$ 
B)  $\frac{-1-6 \sqrt{10}}{19}$ 
C)  $\frac{-1+6 \sqrt{10}}{19}$ 
D)  $\frac{19-6 \sqrt{10}}{-1}$

Question 6

Evaluate the radical function at the given value of the variable.
-$f(x)=\sqrt{x+9}+\sqrt{x}$; find $f(16)$.

Accepted Answer

A)  7 
B)  3 
C)  9 
D)  6 
A)  7 
B)  3 
C)  9 
D)  6

Question 7

Multiply. Write your answer in a +bi form.
-$(3+9 \mathrm{i})(2+7 \mathrm{i})$

Accepted Answer

A)  $69-3 \mathrm{i}$ 
B)  $-57+39 i$ 
C)  -57 - $39 i$ 
D)  $63 i^{2}+39 i+6$ 
A)  $69-3 \mathrm{i}$ 
B)  $-57+39 i$ 
C)  -57 - $39 i$ 
D)  $63 i^{2}+39 i+6$

Question 8

Find the missing number
-$\frac{\sqrt{?}}{\sqrt{5}}=8$

Accepted Answer

A)  $8 \sqrt{5}$ 
B)  40 
C)  $\frac{8}{5}$ 
D)  320 
A)  $8 \sqrt{5}$ 
B)  40 
C)  $\frac{8}{5}$ 
D)  320

Question 9

Can the sum be simplified without first simplifying the individual radical expressions? $6 \sqrt[10]{196}+5 \sqrt[10]{400}$

Accepted Answer

A) True 
 B)False

Question 10

Solve. Check for extraneous solutions.
-$(\mathrm{x}-2)^{1 / 4}+6=0$

Accepted Answer

A)  $\{648\}$ 
B)  $\{-3\}$ 
C)  $\{-648\}$ 
D)  $\varnothing$ 
A)  $\{648\}$ 
B)  $\{-3\}$ 
C)  $\{-648\}$ 
D)  $\varnothing$

Question 11

Simplify by rationalizing the denominator. Write your answer in a + bi form.
-$\frac{4-5 i}{5+2 i}$

Accepted Answer

A)  $\frac{30}{29}+\frac{17}{29} \mathrm{i}$ 
B)  $\frac{10}{21}+\frac{11}{7} \mathrm{i}$ 
C)  $\frac{10}{29}-\frac{33}{29} \mathrm{i}$ 
D)  $\frac{10}{7}+\frac{11}{7} \mathrm{i}$ 
A)  $\frac{30}{29}+\frac{17}{29} \mathrm{i}$ 
B)  $\frac{10}{21}+\frac{11}{7} \mathrm{i}$ 
C)  $\frac{10}{29}-\frac{33}{29} \mathrm{i}$ 
D)  $\frac{10}{7}+\frac{11}{7} \mathrm{i}$

Question 12

Multiply. Write your answer in a +bi form.
-$(7-4 \mathrm{i})(9+4 \mathrm{i})$

Accepted Answer

A)  $79-8 \mathrm{i}$ 
B)  $47-64 \mathrm{i}$ 
C)  $-16 i^{2}-8 i+63$ 
D)  $79+8 \mathrm{i}$ 
A)  $79-8 \mathrm{i}$ 
B)  $47-64 \mathrm{i}$ 
C)  $-16 i^{2}-8 i+63$ 
D)  $79+8 \mathrm{i}$

Question 13

The length of the diagonal of a box is given by $D=\sqrt{\mathrm{L}^{2}+\mathrm{W}^{2}+\mathrm{H}^{2}}$ where $\mathrm{L}, \mathrm{W}$, and $\mathrm{H}$ are the length, width, and height of the box. Find the length of the diagonal, D, of a box that is $2 \mathrm{ft}$ long, $2 \mathrm{ft}$ high, and $4 \mathrm{ft}$ wide. Give the exact value.

Accepted Answer

A)  $8 \mathrm{ft}$ 
B)  $2 \sqrt{6} \mathrm{ft}$ 
C)  $16 \mathrm{ft}$ 
D)  $4 \mathrm{ft}$ 
A)  $8 \mathrm{ft}$ 
B)  $2 \sqrt{6} \mathrm{ft}$ 
C)  $16 \mathrm{ft}$ 
D)  $4 \mathrm{ft}$

Question 14

$\sqrt{-864}$

Accepted Answer

A)  $-12 \sqrt{6}$ 
B)  $-12 \sqrt{-6}$ 
C)  $12 \sqrt{6}$ 
D)  Not a real number 
A)  $-12 \sqrt{6}$ 
B)  $-12 \sqrt{-6}$ 
C)  $12 \sqrt{6}$ 
D)  Not a real number

Question 15

Rewrite as a radical expression and simplify if possible. Assume all variables represent nonnegative real numbers.
-$\left(64 \mathrm{~h}^{20} \mathrm{k}^{22}\right)^{3 / 2}$

Accepted Answer

A)  $512 \mathrm{k}^{30} \mathrm{~h} 3$ 
B)  $512 \mathrm{k}^{30} \mathrm{~h} 30$ 
C)  $64 \mathrm{k}^{30} \mathrm{~h}^{33}$ 
D)  $512 \mathrm{~h} 30_{\mathrm{k}} 33$ 
A)  $512 \mathrm{k}^{30} \mathrm{~h} 3$ 
B)  $512 \mathrm{k}^{30} \mathrm{~h} 30$ 
C)  $64 \mathrm{k}^{30} \mathrm{~h}^{33}$ 
D)  $512 \mathrm{~h} 30_{\mathrm{k}} 33$

Question 16

Simplify the expression. Assume all variables represent nonnegative real numbers.
-$25^{-1 / 2}$

Accepted Answer

A)  5 
B)  -5 
C)  $\frac{1}{5}$ 
D)  $-\frac{1}{5}$ 
A)  5 
B)  -5 
C)  $\frac{1}{5}$ 
D)  $-\frac{1}{5}$

Question 17

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

Accepted Answer

A)  $\{6,13\}$ 
B)  $\{1,13\}$ 
C)  $\{6\}$ 
D)  $\{1,6\}$ 
A)  $\{6,13\}$ 
B)  $\{1,13\}$ 
C)  $\{6\}$ 
D)  $\{1,6\}$

Question 18

$i=-1$

Accepted Answer

A) True 
 B)False

Question 19

Simplify the radical expression. Assume all variables represent nonnegative real numbers.
-$-\sqrt[3]{-512}$

Accepted Answer

A)  -64 
B)  23 
C)  -8 
D)  8 
A)  -64 
B)  23 
C)  -8 
D)  8

Question 20

$4 \sqrt{125}-3 \sqrt{28}-\sqrt{245}+3 \sqrt{847}$

Accepted Answer

A)  $13 \sqrt{5}-27 \sqrt{7}$ 
B)  $-13 \sqrt{5}-27 \sqrt{7}$ 
C)  $-13 \sqrt{5}+27 \sqrt{7}$ 
D)  $13 \sqrt{5}+27 \sqrt{7}$ 
A)  $13 \sqrt{5}-27 \sqrt{7}$ 
B)  $-13 \sqrt{5}-27 \sqrt{7}$ 
C)  $-13 \sqrt{5}+27 \sqrt{7}$ 
D)  $13 \sqrt{5}+27 \sqrt{7}$

Multiply. Write your answer in a +bi form. - $4 \mathrm{i}(8-9 \mathrm{i})$

$\frac{\mathrm{i}^{40}}{\mathrm{i}^{38}}$

Choose values for $n$ , a, and $b$ to demonstrate the truth or falsity of the statement: $\sqrt[n]{\mathrm{a}}+\sqrt[n]{\mathrm{b}}=\sqrt[n]{\mathrm{a}+\mathrm{b}}$

Rationalize the denominator and simplify. - $\frac{3-\sqrt{10}}{3+\sqrt{10}}$

Evaluate the radical function at the given value of the variable. - $f(x)=\sqrt{x+9}+\sqrt{x}$ ; find $f(16)$ .

Multiply. Write your answer in a +bi form. - $(3+9 \mathrm{i})(2+7 \mathrm{i})$

Find the missing number - $\frac{\sqrt{?}}{\sqrt{5}}=8$

Can the sum be simplified without first simplifying the individual radical expressions? $6 \sqrt[10]{196}+5 \sqrt[10]{400}$

Solve. Check for extraneous solutions. - $(\mathrm{x}-2)^{1 / 4}+6=0$

Simplify by rationalizing the denominator. Write your answer in a + bi form. - $\frac{4-5 i}{5+2 i}$

Multiply. Write your answer in a +bi form. - $(7-4 \mathrm{i})(9+4 \mathrm{i})$

$\sqrt{-864}$

Rewrite as a radical expression and simplify if possible. Assume all variables represent nonnegative real numbers. - $\left(64 \mathrm{~h}^{20} \mathrm{k}^{22}\right)^{3 / 2}$

Simplify the expression. Assume all variables represent nonnegative real numbers. - $25^{-1 / 2}$

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

$i=-1$

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - $-\sqrt[3]{-512}$

$4 \sqrt{125}-3 \sqrt{28}-\sqrt{245}+3 \sqrt{847}$

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

Multiply. Write your answer in a +bi form. - 4i(8−9i)4 \mathrm{i}(8-9 \mathrm{i})4i(8−9i)

i40i38\frac{\mathrm{i}^{40}}{\mathrm{i}^{38}}i38i40​

Choose values for nnn , a, and bbb to demonstrate the truth or falsity of the statement: an+bn=a+bn\sqrt[n]{\mathrm{a}}+\sqrt[n]{\mathrm{b}}=\sqrt[n]{\mathrm{a}+\mathrm{b}}na​+nb​=na+b​

Rationalize the denominator and simplify. - 3−103+10\frac{3-\sqrt{10}}{3+\sqrt{10}}3+10​3−10​​

Evaluate the radical function at the given value of the variable. - f(x)=x+9+xf(x)=\sqrt{x+9}+\sqrt{x}f(x)=x+9​+x​ ; find f(16)f(16)f(16) .

Multiply. Write your answer in a +bi form. - (3+9i)(2+7i)(3+9 \mathrm{i})(2+7 \mathrm{i})(3+9i)(2+7i)

Find the missing number - ?5=8\frac{\sqrt{?}}{\sqrt{5}}=85​?​​=8

Can the sum be simplified without first simplifying the individual radical expressions? 619610+5400106 \sqrt[10]{196}+5 \sqrt[10]{400}610196​+510400​

Solve. Check for extraneous solutions. - (x−2)1/4+6=0(\mathrm{x}-2)^{1 / 4}+6=0(x−2)1/4+6=0

Simplify by rationalizing the denominator. Write your answer in a + bi form. - 4−5i5+2i\frac{4-5 i}{5+2 i}5+2i4−5i​

Multiply. Write your answer in a +bi form. - (7−4i)(9+4i)(7-4 \mathrm{i})(9+4 \mathrm{i})(7−4i)(9+4i)

−864\sqrt{-864}−864​

Rewrite as a radical expression and simplify if possible. Assume all variables represent nonnegative real numbers. - (64 h20k22)3/2\left(64 \mathrm{~h}^{20} \mathrm{k}^{22}\right)^{3 / 2}(64 h20k22)3/2

Simplify the expression. Assume all variables represent nonnegative real numbers. - 25−1/225^{-1 / 2}25−1/2

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

i=−1i=-1i=−1

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - −−5123-\sqrt[3]{-512}−3−512​

4125−328−245+38474 \sqrt{125}-3 \sqrt{28}-\sqrt{245}+3 \sqrt{847}4125​−328​−245​+3847​

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

Multiply. Write your answer in a +bi form. - $4 \mathrm{i}(8-9 \mathrm{i})$

$\frac{\mathrm{i}^{40}}{\mathrm{i}^{38}}$

Choose values for $n$ , a, and $b$ to demonstrate the truth or falsity of the statement: $\sqrt[n]{\mathrm{a}}+\sqrt[n]{\mathrm{b}}=\sqrt[n]{\mathrm{a}+\mathrm{b}}$

Rationalize the denominator and simplify. - $\frac{3-\sqrt{10}}{3+\sqrt{10}}$

Evaluate the radical function at the given value of the variable. - $f(x)=\sqrt{x+9}+\sqrt{x}$ ; find $f(16)$ .

Multiply. Write your answer in a +bi form. - $(3+9 \mathrm{i})(2+7 \mathrm{i})$

Find the missing number - $\frac{\sqrt{?}}{\sqrt{5}}=8$

Can the sum be simplified without first simplifying the individual radical expressions? $6 \sqrt[10]{196}+5 \sqrt[10]{400}$

Solve. Check for extraneous solutions. - $(\mathrm{x}-2)^{1 / 4}+6=0$

Simplify by rationalizing the denominator. Write your answer in a + bi form. - $\frac{4-5 i}{5+2 i}$

Multiply. Write your answer in a +bi form. - $(7-4 \mathrm{i})(9+4 \mathrm{i})$

$\sqrt{-864}$

Rewrite as a radical expression and simplify if possible. Assume all variables represent nonnegative real numbers. - $\left(64 \mathrm{~h}^{20} \mathrm{k}^{22}\right)^{3 / 2}$

Simplify the expression. Assume all variables represent nonnegative real numbers. - $25^{-1 / 2}$

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

$i=-1$

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - $-\sqrt[3]{-512}$

$4 \sqrt{125}-3 \sqrt{28}-\sqrt{245}+3 \sqrt{847}$