Question 1

Simplify the radical expression. Assume all variables represent nonnegative real numbers.
-$\sqrt[4]{256}$

Accepted Answer

A)  3 
B)  4 
C)  16 
D)  5 
A)  3 
B)  4 
C)  16 
D)  5

Question 2

Multiply the conjugates.
-$(8+\sqrt{13})(8-\sqrt{13})$

Accepted Answer

A)  $77-16 \sqrt{13}$ 
B)  51 
C)  77 
D)  $77+16 \sqrt{13}$ 
A)  $77-16 \sqrt{13}$ 
B)  51 
C)  77 
D)  $77+16 \sqrt{13}$

Question 3

$(9-6 \mathrm{i}) \div(5+3 \mathrm{i})$

Accepted Answer

A)  $\frac{27}{16}+\frac{57}{16} \mathrm{i}$ 
B)  $\frac{63}{16}+\frac{57}{16} \mathrm{i}$ 
C)  $\frac{63}{34}+\frac{3}{34} \mathrm{i}$ 
D)  $\frac{27}{34}-\frac{57}{34} \mathrm{i}$ 
A)  $\frac{27}{16}+\frac{57}{16} \mathrm{i}$ 
B)  $\frac{63}{16}+\frac{57}{16} \mathrm{i}$ 
C)  $\frac{63}{34}+\frac{3}{34} \mathrm{i}$ 
D)  $\frac{27}{34}-\frac{57}{34} \mathrm{i}$

Question 4

If $a<0$ and $b<0$, then $\sqrt{a} \cdot \sqrt{b}=\sqrt{a b}$.

Accepted Answer

A) True 
 B)False

Question 5

Multiply the conjugates.
-$(-14+3 i)(-14-3 i)$

Accepted Answer

A)  -17 
B)  187 
C)  205 
D)  - 11 
A)  -17 
B)  187 
C)  205 
D)  - 11

Question 6

Choose the one alternative that best completes the statement or answers thequestion.
Express in terms of i.
-$\sqrt{-296}$

Accepted Answer

A)  $2 \sqrt{74}$ 
B)  $-2 \sqrt{74}$ 
C)  $2 \sqrt{74} \mathrm{i}$ 
D)  $-2 \sqrt{74} \mathrm{i}$ 
A)  $2 \sqrt{74}$ 
B)  $-2 \sqrt{74}$ 
C)  $2 \sqrt{74} \mathrm{i}$ 
D)  $-2 \sqrt{74} \mathrm{i}$

Question 7

Simplify by rationalizing the denominator. Write your answer in a + bi form.
-$\frac{10 \mathrm{i}}{8+10 \mathrm{i}}$

Accepted Answer

A)  $\frac{25}{9}-\frac{20}{9} \mathrm{i}$ 
B)  $-\frac{25}{9}-\frac{20}{9} \mathrm{i}$ 
C)  $-\frac{25}{41}+\frac{20}{41} \mathrm{i}$ 
D)  $\frac{25}{41}+\frac{20}{41} \mathrm{i}$ 
A)  $\frac{25}{9}-\frac{20}{9} \mathrm{i}$ 
B)  $-\frac{25}{9}-\frac{20}{9} \mathrm{i}$ 
C)  $-\frac{25}{41}+\frac{20}{41} \mathrm{i}$ 
D)  $\frac{25}{41}+\frac{20}{41} \mathrm{i}$

Question 8

Add or subtract the complex numbers
-$(3-2 \mathrm{i})+(9+8 \mathrm{i})$

Accepted Answer

A)  $-12-6 i$ 
B)  $-6+10 \mathrm{i}$ 
C)  $12+6 i$ 
D)  $12-6 i$ 
A)  $-12-6 i$ 
B)  $-6+10 \mathrm{i}$ 
C)  $12+6 i$ 
D)  $12-6 i$

Question 9

A ssume all variables represent nonnegative real numbers.
-$\sqrt{3}(\sqrt{7}-\sqrt{5})$

Accepted Answer

A)  $\sqrt{36}$ 
B)  $12 \sqrt{3}$ 
C)  $3 \sqrt{7}+3 \sqrt{5}$ 
D)  $\sqrt{21}-\sqrt{15}$ 
A)  $\sqrt{36}$ 
B)  $12 \sqrt{3}$ 
C)  $3 \sqrt{7}+3 \sqrt{5}$ 
D)  $\sqrt{21}-\sqrt{15}$

Question 10

A ssume all variables represent nonnegative real numbers.
-$\sqrt[3]{6}(6 \sqrt[3]{6}-\sqrt[3]{36})$

Accepted Answer

A)  $6 \sqrt[3]{6}-6 \sqrt[3]{6}$ 
B)  $6 \sqrt[3]{36}-6$ 
C)  $5 \sqrt[3]{36}$ 
D)  $6 \sqrt[3]{6}-6$ 
A)  $6 \sqrt[3]{6}-6 \sqrt[3]{6}$ 
B)  $6 \sqrt[3]{36}-6$ 
C)  $5 \sqrt[3]{36}$ 
D)  $6 \sqrt[3]{6}-6$

Question 11

Solve. Check for extraneous solutions.
-$\sqrt{2 x+3}+\sqrt{4-x}=4$

Accepted Answer

A)  $\{-3\}$ 
B)  $\{3\}$. 
C)  $\left\{3, \frac{11}{9}\right\}$ 
D)  $\varnothing$ 
A)  $\{-3\}$ 
B)  $\{3\}$. 
C)  $\left\{3, \frac{11}{9}\right\}$ 
D)  $\varnothing$

Question 12

Rationalize the denominator and simplify.
-$\frac{4}{9-\sqrt{6}}$

Accepted Answer

A)  $\frac{36+4 \sqrt{6}}{-3}$ 
B)  $\frac{4}{9}-\frac{4}{\sqrt{6}}$ 
C)  $\frac{36-4 \sqrt{6}}{75}$ 
D)  $\frac{36+4 \sqrt{6}}{75}$ 
A)  $\frac{36+4 \sqrt{6}}{-3}$ 
B)  $\frac{4}{9}-\frac{4}{\sqrt{6}}$ 
C)  $\frac{36-4 \sqrt{6}}{75}$ 
D)  $\frac{36+4 \sqrt{6}}{75}$

Question 13

Police use a formula $s=S \sqrt{\frac{1}{L}}$, where Sis the test- car speed and $L$ is the test- skid length, to find the actual speed s in an accident which left a skid mark of l. 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)  $55 \mathrm{mph}$ 
B)  $95 \mathrm{mph}$ 
C)  $37 \mathrm{mph}$ 
D)  $68 \mathrm{mph}$ 
A)  $55 \mathrm{mph}$ 
B)  $95 \mathrm{mph}$ 
C)  $37 \mathrm{mph}$ 
D)  $68 \mathrm{mph}$

Question 14

Multiply. Write your answer in a +bi form.
-$(7-6 i)(2+8 i)$

Accepted Answer

A)  $62-44 \mathrm{i}$ 
B)  $62+44 \mathrm{i}$ 
C)  $-34-68 i$ 
D)  $-48 i^{2}+44 i+14$ 
A)  $62-44 \mathrm{i}$ 
B)  $62+44 \mathrm{i}$ 
C)  $-34-68 i$ 
D)  $-48 i^{2}+44 i+14$

Question 15

Add or subtract the complex numbers
-$(8+4 \mathrm{i})-(-9+\mathrm{i})$

Accepted Answer

A)  $17+3 \mathrm{i}$ 
B)  $-1+5 i$ 
C)  $17-3 \mathrm{i}$ 
D)  - $17-3 \mathrm{i}$ 
A)  $17+3 \mathrm{i}$ 
B)  $-1+5 i$ 
C)  $17-3 \mathrm{i}$ 
D)  - $17-3 \mathrm{i}$

Question 16

The distance $d$ in miles that can be seen on the surface of the ocean is given by $d=1.3 \sqrt{h}$, where $h$ is the height in feet above the surface. How high (to the nearest foot) would a platform have to be to see a distance of 14.5 miles?

Accepted Answer

A)  $124 \mathrm{ft}$ 
B)  $112 \mathrm{ft}$ 
C)  $210 \mathrm{ft}$ 
D)  $273 \mathrm{ft}$ 
A)  $124 \mathrm{ft}$ 
B)  $112 \mathrm{ft}$ 
C)  $210 \mathrm{ft}$ 
D)  $273 \mathrm{ft}$

Question 17

Simplify the radical expression. If appropriate, include absolute values.
-$\sqrt{(b+6)^{2}}$

Accepted Answer

A)  $|b+6|$ 
B)  $b+36$ 
C)  $|b-6|$ 
D)  $\sqrt{b}+6$ 
A)  $|b+6|$ 
B)  $b+36$ 
C)  $|b-6|$ 
D)  $\sqrt{b}+6$

Question 18

Approximate to the nearest thousandth, using a calculator
-$\sqrt{7}$

Accepted Answer

A)  2.646 
B)  2.643 
C)  2.651 
D)  7.000 
A)  2.646 
B)  2.643 
C)  2.651 
D)  7.000

Question 19

Rationalize the denominator and simplify.
-$\frac{2 \sqrt{7}+13 \sqrt{2}}{10 \sqrt{2}-3 \sqrt{7}}$

Accepted Answer

A)  $\frac{59 \sqrt{14}+302}{137}$ 
B)  $\frac{59 \sqrt{14}+6 \sqrt{7}+130 \sqrt{2}}{137}$ 
C)  $\frac{1128}{263}$ 
D)  $\frac{59 \sqrt{14}+302}{263}$ 
A)  $\frac{59 \sqrt{14}+302}{137}$ 
B)  $\frac{59 \sqrt{14}+6 \sqrt{7}+130 \sqrt{2}}{137}$ 
C)  $\frac{1128}{263}$ 
D)  $\frac{59 \sqrt{14}+302}{263}$

Question 20

Rewrite as a radical expression and simplify if possible. Assume all variables represent nonnegative real numbers.
-$343^{1 / 3}$

Accepted Answer

A)  7 
B)  2401 
C)  21 
D)  7203 
A)  7 
B)  2401 
C)  21 
D)  7203

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - $\sqrt[4]{256}$

Multiply the conjugates. - $(8+\sqrt{13})(8-\sqrt{13})$

$(9-6 \mathrm{i}) \div(5+3 \mathrm{i})$

If $a<0$ and $b<0$ , then $\sqrt{a} \cdot \sqrt{b}=\sqrt{a b}$ .

Multiply the conjugates. - $(-14+3 i)(-14-3 i)$

Choose the one alternative that best completes the statement or answers thequestion. Express in terms of i. - $\sqrt{-296}$

Simplify by rationalizing the denominator. Write your answer in a + bi form. - $\frac{10 \mathrm{i}}{8+10 \mathrm{i}}$

Add or subtract the complex numbers - $(3-2 \mathrm{i})+(9+8 \mathrm{i})$

A ssume all variables represent nonnegative real numbers. - $\sqrt{3}(\sqrt{7}-\sqrt{5})$

A ssume all variables represent nonnegative real numbers. - $\sqrt[3]{6}(6 \sqrt[3]{6}-\sqrt[3]{36})$

Solve. Check for extraneous solutions. - $\sqrt{2 x+3}+\sqrt{4-x}=4$

Rationalize the denominator and simplify. - $\frac{4}{9-\sqrt{6}}$

Multiply. Write your answer in a +bi form. - $(7-6 i)(2+8 i)$

Add or subtract the complex numbers - $(8+4 \mathrm{i})-(-9+\mathrm{i})$

The distance $d$ in miles that can be seen on the surface of the ocean is given by $d=1.3 \sqrt{h}$ , where $h$ is the height in feet above the surface. How high (to the nearest foot) would a platform have to be to see a distance of 14.5 miles?

Simplify the radical expression. If appropriate, include absolute values. - $\sqrt{(b+6)^{2}}$

Approximate to the nearest thousandth, using a calculator - $\sqrt{7}$

Rationalize the denominator and simplify. - $\frac{2 \sqrt{7}+13 \sqrt{2}}{10 \sqrt{2}-3 \sqrt{7}}$

Rewrite as a radical expression and simplify if possible. Assume all variables represent nonnegative real numbers. - $343^{1 / 3}$

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 the radical expression. Assume all variables represent nonnegative real numbers. - 2564\sqrt[4]{256}4256​

Multiply the conjugates. - (8+13)(8−13)(8+\sqrt{13})(8-\sqrt{13})(8+13​)(8−13​)

(9−6i)÷(5+3i)(9-6 \mathrm{i}) \div(5+3 \mathrm{i})(9−6i)÷(5+3i)

If a<0a<0a<0 and b<0b<0b<0 , then a⋅b=ab\sqrt{a} \cdot \sqrt{b}=\sqrt{a b}a​⋅b​=ab​ .

Multiply the conjugates. - (−14+3i)(−14−3i)(-14+3 i)(-14-3 i)(−14+3i)(−14−3i)

Choose the one alternative that best completes the statement or answers thequestion. Express in terms of i. - −296\sqrt{-296}−296​

Simplify by rationalizing the denominator. Write your answer in a + bi form. - 10i8+10i\frac{10 \mathrm{i}}{8+10 \mathrm{i}}8+10i10i​

Add or subtract the complex numbers - (3−2i)+(9+8i)(3-2 \mathrm{i})+(9+8 \mathrm{i})(3−2i)+(9+8i)

A ssume all variables represent nonnegative real numbers. - 3(7−5)\sqrt{3}(\sqrt{7}-\sqrt{5})3​(7​−5​)

A ssume all variables represent nonnegative real numbers. - 63(663−363)\sqrt[3]{6}(6 \sqrt[3]{6}-\sqrt[3]{36})36​(636​−336​)

Solve. Check for extraneous solutions. - 2x+3+4−x=4\sqrt{2 x+3}+\sqrt{4-x}=42x+3​+4−x​=4

Rationalize the denominator and simplify. - 49−6\frac{4}{9-\sqrt{6}}9−6​4​

Multiply. Write your answer in a +bi form. - (7−6i)(2+8i)(7-6 i)(2+8 i)(7−6i)(2+8i)

Add or subtract the complex numbers - (8+4i)−(−9+i)(8+4 \mathrm{i})-(-9+\mathrm{i})(8+4i)−(−9+i)

The distance ddd in miles that can be seen on the surface of the ocean is given by d=1.3hd=1.3 \sqrt{h}d=1.3h​ , where hhh is the height in feet above the surface. How high (to the nearest foot) would a platform have to be to see a distance of 14.5 miles?

Simplify the radical expression. If appropriate, include absolute values. - (b+6)2\sqrt{(b+6)^{2}}(b+6)2​

Approximate to the nearest thousandth, using a calculator - 7\sqrt{7}7​

Rationalize the denominator and simplify. - 27+132102−37\frac{2 \sqrt{7}+13 \sqrt{2}}{10 \sqrt{2}-3 \sqrt{7}}102​−37​27​+132​​

Rewrite as a radical expression and simplify if possible. Assume all variables represent nonnegative real numbers. - 3431/3343^{1 / 3}3431/3

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 the radical expression. Assume all variables represent nonnegative real numbers. - $\sqrt[4]{256}$

Multiply the conjugates. - $(8+\sqrt{13})(8-\sqrt{13})$

$(9-6 \mathrm{i}) \div(5+3 \mathrm{i})$

If $a<0$ and $b<0$ , then $\sqrt{a} \cdot \sqrt{b}=\sqrt{a b}$ .

Multiply the conjugates. - $(-14+3 i)(-14-3 i)$

Choose the one alternative that best completes the statement or answers thequestion. Express in terms of i. - $\sqrt{-296}$

Simplify by rationalizing the denominator. Write your answer in a + bi form. - $\frac{10 \mathrm{i}}{8+10 \mathrm{i}}$

Add or subtract the complex numbers - $(3-2 \mathrm{i})+(9+8 \mathrm{i})$

A ssume all variables represent nonnegative real numbers. - $\sqrt{3}(\sqrt{7}-\sqrt{5})$

A ssume all variables represent nonnegative real numbers. - $\sqrt[3]{6}(6 \sqrt[3]{6}-\sqrt[3]{36})$

Solve. Check for extraneous solutions. - $\sqrt{2 x+3}+\sqrt{4-x}=4$

Rationalize the denominator and simplify. - $\frac{4}{9-\sqrt{6}}$

Multiply. Write your answer in a +bi form. - $(7-6 i)(2+8 i)$

Add or subtract the complex numbers - $(8+4 \mathrm{i})-(-9+\mathrm{i})$

The distance $d$ in miles that can be seen on the surface of the ocean is given by $d=1.3 \sqrt{h}$ , where $h$ is the height in feet above the surface. How high (to the nearest foot) would a platform have to be to see a distance of 14.5 miles?

Simplify the radical expression. If appropriate, include absolute values. - $\sqrt{(b+6)^{2}}$

Approximate to the nearest thousandth, using a calculator - $\sqrt{7}$

Rationalize the denominator and simplify. - $\frac{2 \sqrt{7}+13 \sqrt{2}}{10 \sqrt{2}-3 \sqrt{7}}$

Rewrite as a radical expression and simplify if possible. Assume all variables represent nonnegative real numbers. - $343^{1 / 3}$