Question 1

Simplify the following expression and write your answer in radical notation: $$\sqrt{12x^3$y^2z^5$}$$

Accepted Answer

$$2xy z^2$ \sqrt{3xz}$$

Question 2

Given $$f(x) = 2x^2$ + 5x$$, find and simplify the difference quotient $$\frac{f(x+h) - f(x)}{h}.$$

Accepted Answer

$$4x + 5 + 2h$$

Question 3

Solve for $$x$$: $$\frac{2}{x-5} = \frac{-5}{x+1}$$

Accepted Answer

$$x = -1, x = 5 ($$both extraneous)

Question 4

Find the domain of the function $$g(x) = \frac{1}{\sqrt{x}}$$ and express your answer in interval notation.

Accepted Answer

$$(0, \infty)$$

Question 5

Simplify the expression $$\sqrt[4]{625}.$$

Accepted Answer

$$5$$

Question 6

Vanessa hikes 2 mph slower than Xavier. If it takes Xavier to hike 8 miles the same time it takes Vanessa to hike 5 miles, what is the speed of each person?

Accepted Answer

Xavier: 8/3 mph, Vanessa: 2/3 mph

Question 7

Simplify the following expression and write your answer with positive exponents: $$\$$left(16x^5$$y^{-4}$$\$$right)^{1/4}$

Accepted Answer

$$2x^{5/4}/y$

Question 8

Solve for $$x$$: $$\frac{3x+5}{x^2$+3x+2} = \frac{2}{x+1}$$

Accepted Answer

$$x = -2, x = -1 ($$extraneous: $$x = -1)$$

Question 9

Simplify the following: $$\sqrt{(-5y)^4$}$$, assuming $$y is $$any real number.

Accepted Answer

$$25y^2$$

Question 10

Given $$f(x) = \sqrt{5 - 3x}$$, find $$f(1)$$ and $$f(2).$$

Accepted Answer

$$f(1) = 2, f(2) = 1$$

Question 11

Simplify the following and write your answer in radical notation: $$\$$left(4x^3$$y^2$$\$$right)^{1/2}$

Accepted Answer

$$2x^{3/2}y$

Question 12

Mary's road trip consisted of 120 miles of traffic and 180 miles at fast speed. If the total trip took 9 hours and her fast speed was 50 mph, how long was she stuck in traffic?

Accepted Answer

3 hours

Question 13

Simplify the following: $$\sqrt[3]{x^2$y^5z^7$}$$, express your answer in simplest radical form.

Accepted Answer

$$xyz^2$$\sqrt[3]{$$y^2z$$}$$

Question 14

Simplify the following expression: $$\frac{x^2$-4x+12}{x^2$-5x-24} \div \frac{x^2$-25}{x^2$-15}$$

Accepted Answer

$$\frac{(x^2$-4x+12)(x^2-15$$)}{$$(x^2-5x-24)(x^2$-25)}$$

Question 15

Simplify and write your answer in terms of positive exponents: $$\$$left(27x^3$$\$$right)^{2/3}$$

Accepted Answer

$$9x^2$$

Question 16

Perform the operation and simplify: $$\sqrt{60} - \sqrt{245}$$

Accepted Answer

$$2\sqrt{15} - 7\sqrt{5}$$

Question 17

Write $$\sqrt{8x^7$/27b^6$$}$ in simplest radical form.

Accepted Answer

$$\frac{2x^3$\sqrt{x}}{3b^3$}$$

Question 18

If $$f(x) = \frac{x-5}{x+1}$$, for what value of $$x is$$ $$f(x) = 5$$?

Accepted Answer

$$x = 6$$

Question 19

Simplify the following: $$\sqrt[3]{-27}$$

Accepted Answer

$$-3$$

College Algebra Review: Simplification, Functions, Radicals, and Applications

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