Question 1

Simplify the expression $\sqrt{50}$.

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 $x^2 + 6x + 5 = 0$ by factoring.

Accepted Answer

$x = -1,\ x = -5$

Question 5

Which of the following is the solution to $2x^2 + 24x - 18 = 0$ using the quadratic formula?

Accepted Answer

$x = -12 \pm 7\sqrt{2}$

Question 6

Express $\frac{(4x^{-2}y^4)^{1/2}}{y^{-3}}$ in simplest form with only positive exponents.

Accepted Answer

$\frac{y^5}{x}$

Question 7

Simplify $\sqrt{125}$.

Accepted Answer

$5\sqrt{5}$

Question 8

A biologist is studying the growth of a bacteria population modeled by $N = 5t^2 + 10t - 2 = 0$. What are the possible values of $t$ (time in hours) when the population is zero?

Accepted Answer

$t = -5 \pm \sqrt{27}$

Question 9

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

Accepted Answer

$7\sqrt{5}$

Question 10

Solve for $x$: $\sqrt{x+4} + 2\sqrt{x-2} = 3$.

Accepted Answer

$x = 3$

Question 11

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

Accepted Answer

$4\sqrt{2}$

Question 12

Rationalize the denominator and simplify: $\frac{\sqrt{7}}{\sqrt{3}}$.

Accepted Answer

$\frac{\sqrt{21}}{3}$

Question 13

A chemical reaction is modeled by the equation $x^2 - 8x + 16 = 0$. What is the solution for $x$?

Accepted Answer

$x = 4$

Question 14

Simplify the expression $\sqrt{18} - \sqrt{8}$.

Accepted Answer

$\sqrt{2}$

Question 15

Solve for $n$: $\sqrt{n+4} + 2\sqrt{n-2} = 3$.

Accepted Answer

$n = 3$

Question 16

Express $\frac{\sqrt{12}}{\sqrt{27}}$ in simplest form with a rationalized denominator.

Accepted Answer

$\frac{2\sqrt{3}}{9}$

Question 17

Which of the following is the correct simplification of $\sqrt{24}$?

Accepted Answer

$2\sqrt{6}$

Question 18

A projectile is launched and its height $h$ (in meters) after $t$ seconds is given by $h = -4.9t^2 + 20t + 1$. When does it hit the ground?

Accepted Answer

$t = \frac{-20 \pm \sqrt{20^2 - 4(-4.9)(1)}}{2(-4.9)}$

College Algebra Study Guide: Quadratics, Exponents, and Radicals

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