Question 1

Simplify the expression $\sqrt{50}$ and express your answer in simplest radical form.

Accepted Answer

$5\sqrt{2}$

Question 2

Which of the following is the correct simplification of $\sqrt{72}$?

Accepted Answer

$6\sqrt{2}$

Question 3

Rationalize the denominator and simplify: $\frac{1}{\sqrt{7}}$.

Accepted Answer

$\frac{\sqrt{7}}{7}$

Question 4

Solve the quadratic equation $x^2 + 24x - 180 = 0$ by factoring.

Accepted Answer

$x = -30, x = 6$

Question 5

Which of the following is the solution to $x^2 - 6x + 5 = 0$?

Accepted Answer

$x = 1, x = 5$

Question 6

Express $\frac{(4x^{-2}y^4)^{\frac{1}{2}}}{2x^{-1}y}$ in simplest form with only positive exponents.

Accepted Answer

$y^{3}$

Question 7

Solve $\sqrt{5x+9} + 1 = x$ for $x$.

Accepted Answer

$x = 2$

Question 8

Which of the following is the correct simplification of $\sqrt{125}$?

Accepted Answer

$5\sqrt{5}$

Question 9

Perform the operation and express in simplest radical form: $7\sqrt{20} - 5\sqrt{45}$.

Accepted Answer

$14\sqrt{5} - 15\sqrt{5} = -1\sqrt{5}$

Question 10

Solve the quadratic equation $x^2 + 8x + 12 = 0$ using the quadratic formula.

Accepted Answer

$x = -6, x = -2$

Question 11

Which of the following is the correct simplification of $\sqrt{27}$?

Accepted Answer

$3\sqrt{3}$

Question 12

If $x = \sqrt{4} + 2\sqrt{7} - 3$, what is the value of $x$?

Accepted Answer

$2 + 2\sqrt{7} - 3$

Question 13

Which of the following is the correct simplification of $\sqrt{18}$?

Accepted Answer

$3\sqrt{2}$

Question 14

Rationalize and simplify: $\frac{\sqrt{7}}{\sqrt{5}}$.

Accepted Answer

$\frac{\sqrt{35}}{5}$

Question 15

Which of the following is the correct simplification of $\sqrt{32}$?

Accepted Answer

$4\sqrt{2}$

College Algebra Study Guide: Quadratics, Exponents, and Radicals

Study Guide - Practice Questions