Question 1

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

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: $\left(16x^5y^{-4}\right)^{1/4}$

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: $\left(4x^3y^2\right)^{1/2}$

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: $\sqrt[3]{x^2y^5z^7}$, 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

Study Guide - Practice Questions

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