Question 1

Find the domain of the function. Express the answer in interval notation.
-$f(x)=\sqrt[6]{x+8}$

Accepted Answer

A)  $(-\infty,-8)$ 
B)  $(-\infty, 8)$ 
C)  $[8, \infty)$ 
D)  $[-8, \infty)$ 
A)  $(-\infty,-8)$ 
B)  $(-\infty, 8)$ 
C)  $[8, \infty)$ 
D)  $[-8, \infty)$

Question 2

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

-$-8 m^{2} \sqrt[4]{7 m^{3}}-4 m^{2} \sqrt[4]{7 m^{3}}$

Accepted Answer

A)  $12 m^{2} \sqrt[4]{7 m^{3}}$ 
B)  $-12 m^{2} \sqrt[4]{7 m^{3}}$ 
C)  $-12 m^{3} \sqrt[4]{7 m}$ 
D)  Cannot simplify 
A)  $12 m^{2} \sqrt[4]{7 m^{3}}$ 
B)  $-12 m^{2} \sqrt[4]{7 m^{3}}$ 
C)  $-12 m^{3} \sqrt[4]{7 m}$ 
D)  Cannot simplify

Question 3

Factor completely
-$x^{9 / 2}-27 x^{3 / 2}$

Accepted Answer

A)  $x^{3 / 2}\left(x^{3}+18 x+27\right)$ 
B)  $x^{3 / 2}(x-3)\left(x^{2}+3 x-9\right)$ 
C)  $x^{3 / 2}(x-3)\left(x^{2}+3 x+9\right)$ 
D)  $x^{3 / 2}\left(x^{3}+18 x-27\right)$ 
A)  $x^{3 / 2}\left(x^{3}+18 x+27\right)$ 
B)  $x^{3 / 2}(x-3)\left(x^{2}+3 x-9\right)$ 
C)  $x^{3 / 2}(x-3)\left(x^{2}+3 x+9\right)$ 
D)  $x^{3 / 2}\left(x^{3}+18 x-27\right)$

Question 4

The length a spring is stretched from its natural length with work, W foot- pounds, is given by $\mathrm{L}=\sqrt{\frac{2 \mathrm{~W}}{\mathrm{k}}}$
Where $\mathrm{k}$ is a constant for the given spring. If a certain spring has a constant of 54.9, and the spring is to be stretched 4.3 feet from its natural length, how much work will be necessary? Round to the nearest tenth of a foot- pound.

Accepted Answer

A)  1015.1 foot- pounds 
B)  118 foot- pounds 
C)  507.6 foot-pounds 
D)  56.9 foot- pounds 
A)  1015.1 foot- pounds 
B)  118 foot- pounds 
C)  507.6 foot-pounds 
D)  56.9 foot- pounds

Question 5

Rewrite the radical expression using rational exponents. A ssume all variables represent nonnegative real numbers.
-$\sqrt[6]{\mathrm{mn}}$

Accepted Answer

A)  $\frac{1}{(\mathrm{mn})^{6}}$ 
B)  $(\mathrm{mn})^{1 / 6}$ 
C)  $m^{1 / 6} n$ 
D)  $\mathrm{mn}^{1 / 6}$ 
A)  $\frac{1}{(\mathrm{mn})^{6}}$ 
B)  $(\mathrm{mn})^{1 / 6}$ 
C)  $m^{1 / 6} n$ 
D)  $\mathrm{mn}^{1 / 6}$

Question 6

The velocity $\mathrm{v}$ in feet per second of a free- falling object can be found using the formula $\mathrm{v}=\sqrt{64 \mathrm{~d}}$, where $d$ is the distance (in feet) that the object has already fallen. Find the distance that and object with a velocity of $68 \mathrm{ft} / \mathrm{s}$ has fallen. Round to the nearest foot.

Accepted Answer

A)  74 feet 
B)  63 feet 
C)  66 feet 
D)  72 feet 
A)  74 feet 
B)  63 feet 
C)  66 feet 
D)  72 feet

Question 7

For the function $f(x)=\sqrt{x^{2}-8 x+24}-1$, find all values $x$ for which $f(x)=2$.

Accepted Answer

A)  $\{3,-5\}$ 
B)  $\{-3,-5\}$. 
C)  $\{3,5\}$ 
D)  $\varnothing$ 
A)  $\{3,-5\}$ 
B)  $\{-3,-5\}$. 
C)  $\{3,5\}$ 
D)  $\varnothing$

Question 8

Explain the procedure you would use to find the quotient $\frac{4+3 i}{-1+5 i}$. Do not actually find the quotient.

Accepted Answer

Multiply both the numerator and denomina

Question 9

Solve. Check for extraneous solutions.
-$\sqrt{x^{2}+4 x+20}+1=x$

Accepted Answer

A)  $\left\{\frac{6}{19}\right\}$ 
B)  $\left\{\frac{19}{6}\right\}$ 
C)  $\left\{-\frac{19}{6}\right\}$ 
D)  $\varnothing$ 
A)  $\left\{\frac{6}{19}\right\}$ 
B)  $\left\{\frac{19}{6}\right\}$ 
C)  $\left\{-\frac{19}{6}\right\}$ 
D)  $\varnothing$

Question 10

Simplify.
-$\sqrt[3]{49} \cdot \sqrt[3]{7}$

Accepted Answer

A)  $\sqrt[3]{343}$ 
B)  7 
C)  18 
D)  $7 \sqrt[3]{7}$ 
A)  $\sqrt[3]{343}$ 
B)  7 
C)  18 
D)  $7 \sqrt[3]{7}$

Question 11

Multiply the conjugates.
-$(-3+3 \mathrm{i})(-3-3 \mathrm{i})$

Accepted Answer

A)  18 
B)  0 
C)  21 
D)  19 
A)  18 
B)  0 
C)  21 
D)  19

Question 12

Find the missing complex number
-$\frac{?}{4+6 \mathrm{i}}=7+4 \mathrm{i}$

Accepted Answer

A)  $24 \mathrm{i}^{2}+58 \mathrm{i}+28$ 
B)  $52+26 i$ 
C)  $4+58 \mathrm{i}$ 
D)  4 - $58 \mathrm{i}$ 
A)  $24 \mathrm{i}^{2}+58 \mathrm{i}+28$ 
B)  $52+26 i$ 
C)  $4+58 \mathrm{i}$ 
D)  4 - $58 \mathrm{i}$

Question 13

Use the formula $E=2.575 \sqrt{\frac{0.25}{n}}$ to compute the sample size that a statistician requires to estimate a population proportion with $99 \%$ confidence for a margin of error $\mathrm{E}=2.5 \%$.

Accepted Answer

A)  1412 
B)  7957 
C)  10,609 
D)  2652 
A)  1412 
B)  7957 
C)  10,609 
D)  2652

Question 14

Explain why $\sqrt[k]{\mathrm{x}^{\mathrm{k}}}=|\mathrm{x}|$ when $\mathrm{k}$ is even but $\sqrt[k]{\mathrm{x}^{\mathrm{k}}}=\mathrm{x}$ when $\mathrm{k}$ is odd.

Accepted Answer

When @#LAT-DLM& is even, @#LAT-DLM& represents a nonnegative

Question 15

Simplify the expression. Assume all variables represent nonnegative real numbers.
-$\sqrt[5]{3} \cdot \sqrt{7}$

Accepted Answer

A)  $\sqrt[7]{21}$ 
B)  $\sqrt[7]{11}$ 
C)  $\sqrt[10]{151,263}$ 
D)  $\sqrt[10]{21}$ 
A)  $\sqrt[7]{21}$ 
B)  $\sqrt[7]{11}$ 
C)  $\sqrt[10]{151,263}$ 
D)  $\sqrt[10]{21}$

Question 16

The distance $d$ in miles that can be seen on the surface of the ocean is given by $d=1.2 \sqrt{h}$, 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 16.5 miles?

Accepted Answer

A)  $138 \mathrm{ft}$ 
B)  $189 \mathrm{ft}$ 
C)  $326 \mathrm{ft}$ 
D)  $272 \mathrm{ft}$ 
A)  $138 \mathrm{ft}$ 
B)  $189 \mathrm{ft}$ 
C)  $326 \mathrm{ft}$ 
D)  $272 \mathrm{ft}$

Question 17

Add or subtract the complex numbers
-$(2+2 \mathrm{i})-(6+9 \mathrm{i})+(8+9 \mathrm{i})$

Accepted Answer

A)  $-12-16 \mathrm{i}$ 
B)  $-12+2 \mathrm{i}$ 
C)  $4+2 \mathrm{i}$ 
D)  $4+20 \mathrm{i}$ 
A)  $-12-16 \mathrm{i}$ 
B)  $-12+2 \mathrm{i}$ 
C)  $4+2 \mathrm{i}$ 
D)  $4+20 \mathrm{i}$

Question 18

What value of $x$ will make the following equation true? Explain your answer.
$\sqrt{-4 \mathrm{x}-3}+\sqrt{12 \mathrm{x}+9}=0$

Accepted Answer

@#LAT-DLM&. Since neither square root can have a v

Question 19

Simplify.
-$\frac{\sqrt[3]{640}}{\sqrt[3]{10}}$

Accepted Answer

A)  3 
B)  4 
C)  5 
D)  6 
A)  3 
B)  4 
C)  5 
D)  6

Question 20

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

-$3 \sqrt[3]{\mathrm{a}}+\sqrt[3]{27 \mathrm{a}}$

Accepted Answer

A)  $4 \sqrt[3]{27 a}$ 
B)  $3 \sqrt[3]{a}+\sqrt[3]{27 a}$ 
C)  $9 \sqrt[3]{\mathrm{a}}$ 
D)  $6 \sqrt[3]{\mathrm{a}}$ 
A)  $4 \sqrt[3]{27 a}$ 
B)  $3 \sqrt[3]{a}+\sqrt[3]{27 a}$ 
C)  $9 \sqrt[3]{\mathrm{a}}$ 
D)  $6 \sqrt[3]{\mathrm{a}}$

Find the domain of the function. Express the answer in interval notation. - $f(x)=\sqrt[6]{x+8}$

Add or subtract. Assume all variables represent nonnegative real numbers. - $-8 m^{2} \sqrt[4]{7 m^{3}}-4 m^{2} \sqrt[4]{7 m^{3}}$

Factor completely - $x^{9 / 2}-27 x^{3 / 2}$

Rewrite the radical expression using rational exponents. A ssume all variables represent nonnegative real numbers. - $\sqrt[6]{\mathrm{mn}}$

For the function $f(x)=\sqrt{x^{2}-8 x+24}-1$ , find all values $x$ for which $f(x)=2$ .

Explain the procedure you would use to find the quotient $\frac{4+3 i}{-1+5 i}$ . Do not actually find the quotient.

Solve. Check for extraneous solutions. - $\sqrt{x^{2}+4 x+20}+1=x$

Simplify. - $\sqrt[3]{49} \cdot \sqrt[3]{7}$

Multiply the conjugates. - $(-3+3 \mathrm{i})(-3-3 \mathrm{i})$

Find the missing complex number - $\frac{?}{4+6 \mathrm{i}}=7+4 \mathrm{i}$

Use the formula $E=2.575 \sqrt{\frac{0.25}{n}}$ to compute the sample size that a statistician requires to estimate a population proportion with $99 \%$ confidence for a margin of error $\mathrm{E}=2.5 \%$ .

Explain why $\sqrt[k]{\mathrm{x}^{\mathrm{k}}}=|\mathrm{x}|$ when $\mathrm{k}$ is even but $\sqrt[k]{\mathrm{x}^{\mathrm{k}}}=\mathrm{x}$ when $\mathrm{k}$ is odd.

Simplify the expression. Assume all variables represent nonnegative real numbers. - $\sqrt[5]{3} \cdot \sqrt{7}$

The distance $d$ in miles that can be seen on the surface of the ocean is given by $d=1.2 \sqrt{h}$ , 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 16.5 miles?

Add or subtract the complex numbers - $(2+2 \mathrm{i})-(6+9 \mathrm{i})+(8+9 \mathrm{i})$

What value of $x$ will make the following equation true? Explain your answer. $\sqrt{-4 \mathrm{x}-3}+\sqrt{12 \mathrm{x}+9}=0$

Simplify. - $\frac{\sqrt[3]{640}}{\sqrt[3]{10}}$

Add or subtract. Assume all variables represent nonnegative real numbers. - $3 \sqrt[3]{\mathrm{a}}+\sqrt[3]{27 \mathrm{a}}$

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 domain of the function. Express the answer in interval notation. - f(x)=x+86f(x)=\sqrt[6]{x+8}f(x)=6x+8​

Add or subtract. Assume all variables represent nonnegative real numbers. - −8m27m34−4m27m34-8 m^{2} \sqrt[4]{7 m^{3}}-4 m^{2} \sqrt[4]{7 m^{3}}−8m247m3​−4m247m3​

Factor completely - x9/2−27x3/2x^{9 / 2}-27 x^{3 / 2}x9/2−27x3/2

Rewrite the radical expression using rational exponents. A ssume all variables represent nonnegative real numbers. - mn6\sqrt[6]{\mathrm{mn}}6mn​

For the function f(x)=x2−8x+24−1f(x)=\sqrt{x^{2}-8 x+24}-1f(x)=x2−8x+24​−1 , find all values xxx for which f(x)=2f(x)=2f(x)=2 .

Explain the procedure you would use to find the quotient 4+3i−1+5i\frac{4+3 i}{-1+5 i}−1+5i4+3i​ . Do not actually find the quotient.

Solve. Check for extraneous solutions. - x2+4x+20+1=x\sqrt{x^{2}+4 x+20}+1=xx2+4x+20​+1=x

Simplify. - 493⋅73\sqrt[3]{49} \cdot \sqrt[3]{7}349​⋅37​

Multiply the conjugates. - (−3+3i)(−3−3i)(-3+3 \mathrm{i})(-3-3 \mathrm{i})(−3+3i)(−3−3i)

Find the missing complex number - ?4+6i=7+4i\frac{?}{4+6 \mathrm{i}}=7+4 \mathrm{i}4+6i?​=7+4i

Use the formula E=2.5750.25nE=2.575 \sqrt{\frac{0.25}{n}}E=2.575n0.25​​ to compute the sample size that a statistician requires to estimate a population proportion with 99%99 \%99% confidence for a margin of error E=2.5%\mathrm{E}=2.5 \%E=2.5% .

Explain why xkk=∣x∣\sqrt[k]{\mathrm{x}^{\mathrm{k}}}=|\mathrm{x}|kxk​=∣x∣ when k\mathrm{k}k is even but xkk=x\sqrt[k]{\mathrm{x}^{\mathrm{k}}}=\mathrm{x}kxk​=x when k\mathrm{k}k is odd.

Simplify the expression. Assume all variables represent nonnegative real numbers. - 35⋅7\sqrt[5]{3} \cdot \sqrt{7}53​⋅7​

The distance ddd in miles that can be seen on the surface of the ocean is given by d=1.2hd=1.2 \sqrt{h}d=1.2h​ , 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 16.5 miles?

Add or subtract the complex numbers - (2+2i)−(6+9i)+(8+9i)(2+2 \mathrm{i})-(6+9 \mathrm{i})+(8+9 \mathrm{i})(2+2i)−(6+9i)+(8+9i)

What value of xxx will make the following equation true? Explain your answer. −4x−3+12x+9=0\sqrt{-4 \mathrm{x}-3}+\sqrt{12 \mathrm{x}+9}=0−4x−3​+12x+9​=0

Simplify. - 6403103\frac{\sqrt[3]{640}}{\sqrt[3]{10}}310​3640​​

Add or subtract. Assume all variables represent nonnegative real numbers. - 3a3+27a33 \sqrt[3]{\mathrm{a}}+\sqrt[3]{27 \mathrm{a}}33a​+327a​

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

Find the domain of the function. Express the answer in interval notation. - $f(x)=\sqrt[6]{x+8}$

Add or subtract. Assume all variables represent nonnegative real numbers. - $-8 m^{2} \sqrt[4]{7 m^{3}}-4 m^{2} \sqrt[4]{7 m^{3}}$

Factor completely - $x^{9 / 2}-27 x^{3 / 2}$

Rewrite the radical expression using rational exponents. A ssume all variables represent nonnegative real numbers. - $\sqrt[6]{\mathrm{mn}}$

For the function $f(x)=\sqrt{x^{2}-8 x+24}-1$ , find all values $x$ for which $f(x)=2$ .

Explain the procedure you would use to find the quotient $\frac{4+3 i}{-1+5 i}$ . Do not actually find the quotient.

Solve. Check for extraneous solutions. - $\sqrt{x^{2}+4 x+20}+1=x$

Simplify. - $\sqrt[3]{49} \cdot \sqrt[3]{7}$

Multiply the conjugates. - $(-3+3 \mathrm{i})(-3-3 \mathrm{i})$

Find the missing complex number - $\frac{?}{4+6 \mathrm{i}}=7+4 \mathrm{i}$

Use the formula $E=2.575 \sqrt{\frac{0.25}{n}}$ to compute the sample size that a statistician requires to estimate a population proportion with $99 \%$ confidence for a margin of error $\mathrm{E}=2.5 \%$ .

Explain why $\sqrt[k]{\mathrm{x}^{\mathrm{k}}}=|\mathrm{x}|$ when $\mathrm{k}$ is even but $\sqrt[k]{\mathrm{x}^{\mathrm{k}}}=\mathrm{x}$ when $\mathrm{k}$ is odd.

Simplify the expression. Assume all variables represent nonnegative real numbers. - $\sqrt[5]{3} \cdot \sqrt{7}$

The distance $d$ in miles that can be seen on the surface of the ocean is given by $d=1.2 \sqrt{h}$ , 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 16.5 miles?

Add or subtract the complex numbers - $(2+2 \mathrm{i})-(6+9 \mathrm{i})+(8+9 \mathrm{i})$

What value of $x$ will make the following equation true? Explain your answer. $\sqrt{-4 \mathrm{x}-3}+\sqrt{12 \mathrm{x}+9}=0$

Simplify. - $\frac{\sqrt[3]{640}}{\sqrt[3]{10}}$

Add or subtract. Assume all variables represent nonnegative real numbers. - $3 \sqrt[3]{\mathrm{a}}+\sqrt[3]{27 \mathrm{a}}$