Question 1

Simplify. Assume all variables represent nonnegative values.
-$\frac{\sqrt{4}}{\sqrt{49}}$

Accepted Answer

A)  14 
B)  $\frac{2}{7}$ 
C)  1 
D)  $\frac{7}{2}$ 
A)  14 
B)  $\frac{2}{7}$ 
C)  1 
D)  $\frac{7}{2}$

Question 2

Solve. Check for extraneous solutions.
-$\sqrt{3 x+10}=5-2 x$

Accepted Answer

A)  $\left\{\frac{3}{4}\right\}$ 
B)  $\{5\}$ 
C)  $\left\{\frac{3}{4}, 5\right\}$ 
D)  $\left\{\frac{5}{4}, 9\right\}$ 
A)  $\left\{\frac{3}{4}\right\}$ 
B)  $\{5\}$ 
C)  $\left\{\frac{3}{4}, 5\right\}$ 
D)  $\left\{\frac{5}{4}, 9\right\}$

Question 3

Simplify by rationalizing the denominator. Write your answer in a + bi form.
-$\frac{6-6 i}{5-7 i}$

Accepted Answer

A)  $\frac{1}{2}+\frac{1}{4} \mathrm{i}$ 
B)  $\frac{36}{37}+\frac{6}{37} i$ 
C)  $-\frac{3}{2}+\frac{1}{4} \mathrm{i}$ 
D)  $-\frac{12}{37}+\frac{72}{37} \mathrm{i}$ 
A)  $\frac{1}{2}+\frac{1}{4} \mathrm{i}$ 
B)  $\frac{36}{37}+\frac{6}{37} i$ 
C)  $-\frac{3}{2}+\frac{1}{4} \mathrm{i}$ 
D)  $-\frac{12}{37}+\frac{72}{37} \mathrm{i}$

Question 4

Add or subtract. Assume all variables represent nonnegative real numbers.

-$6 \sqrt{80 \mathrm{x}^{2}}-3 \sqrt{45 \mathrm{x}^{2}}-\sqrt{5 \mathrm{x}^{2}}$

Accepted Answer

A)  $14 x \sqrt{5}$ 
B)  $2 x \sqrt{35}$ 
C)  $15 x \sqrt{5}$ 
D)  $3 x \sqrt{35}$ 
A)  $14 x \sqrt{5}$ 
B)  $2 x \sqrt{35}$ 
C)  $15 x \sqrt{5}$ 
D)  $3 x \sqrt{35}$

Question 5

Simplify the difference quotient $\frac{f(x+h)-f(x)}{h}$, and evaluate as $h$ approaches 0 to find the rate of change of $f(x)$.
-$f(x)=\sqrt{7 x+32}$

Accepted Answer

A)  $-\frac{7}{2 \sqrt{7 x+32}}$ 
B)  $-\frac{7}{\sqrt{7 \mathrm{x}+32}}$ 
C)  $\frac{7}{\sqrt{7 \mathrm{x}+32}}$ 
D)  $\frac{7}{2 \sqrt{7 x+32}}$ 
A)  $-\frac{7}{2 \sqrt{7 x+32}}$ 
B)  $-\frac{7}{\sqrt{7 \mathrm{x}+32}}$ 
C)  $\frac{7}{\sqrt{7 \mathrm{x}+32}}$ 
D)  $\frac{7}{2 \sqrt{7 x+32}}$

Question 6

For the function $f(x)=6 \sqrt{2 x-8}-6 \sqrt{x+5}$, find all values $x$ for which $f(x)=-18$.

Accepted Answer

A)  4 
B)  -11 
C)  18 
D)  11 
A)  4 
B)  -11 
C)  18 
D)  11

Question 7

Can the sum be simplified without first simplifying the individual radical expressions? $6 \sqrt[10]{3}+3 \sqrt[10]{3}$

Accepted Answer

A) True 
 B)False

Question 8

Give the definition or an example of the phrase: Rationalizing the numerator.

Accepted Answer

The process of remov

Question 9

Simplify the radical expression. Assume all variables represent nonnegative real numbers.
-$\sqrt[3]{64 a^{8} b^{5}}$

Accepted Answer

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

Question 10

$i^{17}$

Accepted Answer

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

Question 11

Police use a formula $s=S \sqrt{\frac{l}{L}}$, where Sis the test- car speed and $L$ is the test- skid length, to find the actual speed $\mathrm{s}$ in an accident which left a skid mark of 1 . Find the speed (nearest whole mph) when $\mathrm{S}=45 \mathrm{mph}, \mathrm{l}=150 \mathrm{ft}, \mathrm{L}=100 \mathrm{ft}$.

Accepted Answer

A)  $37 \mathrm{mph}$ 
B)  $68 \mathrm{mph}$ 
C)  $55 \mathrm{mph}$ 
D)  $95 \mathrm{mph}$ 
A)  $37 \mathrm{mph}$ 
B)  $68 \mathrm{mph}$ 
C)  $55 \mathrm{mph}$ 
D)  $95 \mathrm{mph}$

Question 12

The length of the diagonal of a box is given by $D=\sqrt{L^{2}+W^{2}+H^{2}}$ where $L, W$, and $H$ are the length, width, and height of the box. Find the length of the diagonal, D, of a box that is $1 \mathrm{ft}$ long, $5 \mathrm{ft}$ high, and $4 \mathrm{ft}$ wide. Give the exact value.

Accepted Answer

A)  $2 \sqrt{5} \mathrm{ft}$ 
B)  $10 \mathrm{ft}$ 
C)  $20 \mathrm{ft}$ 
D)  $\sqrt{42} \mathrm{ft}$ 
A)  $2 \sqrt{5} \mathrm{ft}$ 
B)  $10 \mathrm{ft}$ 
C)  $20 \mathrm{ft}$ 
D)  $\sqrt{42} \mathrm{ft}$

Question 13

Simplify by rationalizing the denominator. Write your answer in a + bi form.
-$\frac{-19+8 i}{-18 i}$

Accepted Answer

A)  $\frac{4}{9}+\frac{19}{18} \mathrm{i}$ 
B)  $\frac{4}{9}-\frac{19}{18} \mathrm{i}$ 
C)  $-\frac{4}{9}-\frac{19}{18} \mathrm{i}$ 
D)  $-\frac{4}{9}+\frac{19}{18} \mathrm{i}$ 
A)  $\frac{4}{9}+\frac{19}{18} \mathrm{i}$ 
B)  $\frac{4}{9}-\frac{19}{18} \mathrm{i}$ 
C)  $-\frac{4}{9}-\frac{19}{18} \mathrm{i}$ 
D)  $-\frac{4}{9}+\frac{19}{18} \mathrm{i}$

Question 14

Find the missing number
-$\sqrt{20} \cdot \sqrt{?}=10$

Accepted Answer

A)  $\frac{5}{2}$ 
B)  10 
C)  $\frac{1}{2}$ 
D)  5 
A)  $\frac{5}{2}$ 
B)  10 
C)  $\frac{1}{2}$ 
D)  5

Question 15

A ssume all variables represent nonnegative real numbers.
-$3 \sqrt{5}(4 \sqrt{5}+5 \sqrt{10})$

Accepted Answer

A)  $60+75 \sqrt{2}$ 
B)  $-60+75 \sqrt{2}$ 
C)  $60+15 \sqrt{50}$ 
D)  $60-75 \sqrt{2}$ 
A)  $60+75 \sqrt{2}$ 
B)  $-60+75 \sqrt{2}$ 
C)  $60+15 \sqrt{50}$ 
D)  $60-75 \sqrt{2}$

Question 16

Solve. Check for extraneous solutions.
-$\sqrt{\mathrm{x}^{2}-5 \mathrm{x}+16}=\mathrm{x}-1$

Accepted Answer

A)  $\left\{-\frac{5}{2}\right\}$ 
B)  $\{4\}$ 
C)  $\{-5\}$ 
D)  $\{5\}$. 
A)  $\left\{-\frac{5}{2}\right\}$ 
B)  $\{4\}$ 
C)  $\{-5\}$ 
D)  $\{5\}$.

Question 17

$i^{14}$

Accepted Answer

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

Question 18

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

Accepted Answer

A)  $-5 x$ 
B)  $25 x^{2}$ 
C)  $5 x^{2}$ 
D)  $25 x$ 
A)  $-5 x$ 
B)  $25 x^{2}$ 
C)  $5 x^{2}$ 
D)  $25 x$

Question 19

The length of the diagonal of a rectangle is given by $D=\sqrt{L^{2}+W^{2}}$ where $L$ and $W$ are the length and width of the rectangle. What is the length of the diagonal, D, of a rectangle that is 16 inches long and 2 inches wide? Round your answer to the nearest tenth of an inch, if necessary.

Accepted Answer

A)  15.9 inches 
B)  5.7 inches 
C)  4.2 inches 
D)  16.1 inches 
A)  15.9 inches 
B)  5.7 inches 
C)  4.2 inches 
D)  16.1 inches

Question 20

Rewrite as a radical expression and simplify if possible. Assume all variables represent nonnegative real numbers.
-$(-27)^{2 / 3}$

Accepted Answer

A)  -9 
B)  -3 
C)  9 
D)  Not a real number 
A)  -9 
B)  -3 
C)  9 
D)  Not a real number

Simplify. Assume all variables represent nonnegative values. - $\frac{\sqrt{4}}{\sqrt{49}}$

Solve. Check for extraneous solutions. - $\sqrt{3 x+10}=5-2 x$

Simplify by rationalizing the denominator. Write your answer in a + bi form. - $\frac{6-6 i}{5-7 i}$

Add or subtract. Assume all variables represent nonnegative real numbers. - $6 \sqrt{80 \mathrm{x}^{2}}-3 \sqrt{45 \mathrm{x}^{2}}-\sqrt{5 \mathrm{x}^{2}}$

Simplify the difference quotient $\frac{f(x+h)-f(x)}{h}$ , and evaluate as $h$ approaches 0 to find the rate of change of $f(x)$ . - $f(x)=\sqrt{7 x+32}$

For the function $f(x)=6 \sqrt{2 x-8}-6 \sqrt{x+5}$ , find all values $x$ for which $f(x)=-18$ .

Can the sum be simplified without first simplifying the individual radical expressions? $6 \sqrt[10]{3}+3 \sqrt[10]{3}$

Give the definition or an example of the phrase: Rationalizing the numerator.

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - $\sqrt[3]{64 a^{8} b^{5}}$

$i^{17}$

The length of the diagonal of a box is given by $D=\sqrt{L^{2}+W^{2}+H^{2}}$ where $L, W$ , and $H$ are the length, width, and height of the box. Find the length of the diagonal, D, of a box that is $1 \mathrm{ft}$ long, $5 \mathrm{ft}$ high, and $4 \mathrm{ft}$ wide. Give the exact value.

Simplify by rationalizing the denominator. Write your answer in a + bi form. - $\frac{-19+8 i}{-18 i}$

Find the missing number - $\sqrt{20} \cdot \sqrt{?}=10$

A ssume all variables represent nonnegative real numbers. - $3 \sqrt{5}(4 \sqrt{5}+5 \sqrt{10})$

Solve. Check for extraneous solutions. - $\sqrt{\mathrm{x}^{2}-5 \mathrm{x}+16}=\mathrm{x}-1$

$i^{14}$

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

The length of the diagonal of a rectangle is given by $D=\sqrt{L^{2}+W^{2}}$ where $L$ and $W$ are the length and width of the rectangle. What is the length of the diagonal, D, of a rectangle that is 16 inches long and 2 inches wide? Round your answer to the nearest tenth of an inch, if necessary.

Rewrite as a radical expression and simplify if possible. Assume all variables represent nonnegative real numbers. - $(-27)^{2 / 3}$

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. Assume all variables represent nonnegative values. - 449\frac{\sqrt{4}}{\sqrt{49}}49​4​​

Solve. Check for extraneous solutions. - 3x+10=5−2x\sqrt{3 x+10}=5-2 x3x+10​=5−2x

Simplify by rationalizing the denominator. Write your answer in a + bi form. - 6−6i5−7i\frac{6-6 i}{5-7 i}5−7i6−6i​

Add or subtract. Assume all variables represent nonnegative real numbers. - 680x2−345x2−5x26 \sqrt{80 \mathrm{x}^{2}}-3 \sqrt{45 \mathrm{x}^{2}}-\sqrt{5 \mathrm{x}^{2}}680x2​−345x2​−5x2​

Simplify the difference quotient f(x+h)−f(x)h\frac{f(x+h)-f(x)}{h}hf(x+h)−f(x)​ , and evaluate as hhh approaches 0 to find the rate of change of f(x)f(x)f(x) . - f(x)=7x+32f(x)=\sqrt{7 x+32}f(x)=7x+32​

For the function f(x)=62x−8−6x+5f(x)=6 \sqrt{2 x-8}-6 \sqrt{x+5}f(x)=62x−8​−6x+5​ , find all values xxx for which f(x)=−18f(x)=-18f(x)=−18 .

Can the sum be simplified without first simplifying the individual radical expressions? 6310+33106 \sqrt[10]{3}+3 \sqrt[10]{3}6103​+3103​

Give the definition or an example of the phrase: Rationalizing the numerator.

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - 64a8b53\sqrt[3]{64 a^{8} b^{5}}364a8b5​

i17i^{17}i17

Simplify by rationalizing the denominator. Write your answer in a + bi form. - −19+8i−18i\frac{-19+8 i}{-18 i}−18i−19+8i​

Find the missing number - 20⋅?=10\sqrt{20} \cdot \sqrt{?}=1020​⋅?​=10

A ssume all variables represent nonnegative real numbers. - 35(45+510)3 \sqrt{5}(4 \sqrt{5}+5 \sqrt{10})35​(45​+510​)

Solve. Check for extraneous solutions. - x2−5x+16=x−1\sqrt{\mathrm{x}^{2}-5 \mathrm{x}+16}=\mathrm{x}-1x2−5x+16​=x−1

i14i^{14}i14

Find the missing number - ?=5x\sqrt{?}=5 x?​=5x

Rewrite as a radical expression and simplify if possible. Assume all variables represent nonnegative real numbers. - (−27)2/3(-27)^{2 / 3}(−27)2/3

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. Assume all variables represent nonnegative values. - $\frac{\sqrt{4}}{\sqrt{49}}$

Solve. Check for extraneous solutions. - $\sqrt{3 x+10}=5-2 x$

Simplify by rationalizing the denominator. Write your answer in a + bi form. - $\frac{6-6 i}{5-7 i}$

Add or subtract. Assume all variables represent nonnegative real numbers. - $6 \sqrt{80 \mathrm{x}^{2}}-3 \sqrt{45 \mathrm{x}^{2}}-\sqrt{5 \mathrm{x}^{2}}$

Simplify the difference quotient $\frac{f(x+h)-f(x)}{h}$ , and evaluate as $h$ approaches 0 to find the rate of change of $f(x)$ . - $f(x)=\sqrt{7 x+32}$

For the function $f(x)=6 \sqrt{2 x-8}-6 \sqrt{x+5}$ , find all values $x$ for which $f(x)=-18$ .

Can the sum be simplified without first simplifying the individual radical expressions? $6 \sqrt[10]{3}+3 \sqrt[10]{3}$

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - $\sqrt[3]{64 a^{8} b^{5}}$

$i^{17}$

Simplify by rationalizing the denominator. Write your answer in a + bi form. - $\frac{-19+8 i}{-18 i}$

Find the missing number - $\sqrt{20} \cdot \sqrt{?}=10$

A ssume all variables represent nonnegative real numbers. - $3 \sqrt{5}(4 \sqrt{5}+5 \sqrt{10})$

Solve. Check for extraneous solutions. - $\sqrt{\mathrm{x}^{2}-5 \mathrm{x}+16}=\mathrm{x}-1$

$i^{14}$

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

Rewrite as a radical expression and simplify if possible. Assume all variables represent nonnegative real numbers. - $(-27)^{2 / 3}$