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

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