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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