Question 1

Simplify $$\sqrt{12x^2$}.$$

Accepted Answer

$$2x\sqrt{3}$$

Question 2

Simplify $$\sqrt{40}.$$

Accepted Answer

$$2\sqrt{10}$$

Question 3

Approximate $$\sqrt{60} to 3 $$decimal places.

Accepted Answer

$$7.745$$

Question 4

Simplify $$\sqrt{50} + \sqrt{72}.$$

Accepted Answer

$$5\sqrt{2} + 6\sqrt{2} = 11\sqrt{2}$$

Question 5

For $$g(x) = \sqrt{x-5}$$, find $$g(13)$$ and $$g(7)$$, and state the domain.

Accepted Answer

$$g(13) = 4$$, $$g(7) = \sqrt{2}$$, domain: $$[5, \infty)$$

Question 6

Simplify $$\sqrt{27x^2$}.$$

Accepted Answer

$$3x\sqrt{3}$$

Question 7

Simplify $$\sqrt{50y^2$}.$$

Accepted Answer

$$5y\sqrt{2}$$

Question 8

Rationalize the denominator: $$\frac{\sqrt{21}}{2}.$$

Accepted Answer

$$\frac{\sqrt{21}}{2}$$

Question 9

Rationalize the denominator: $$\frac{\sqrt{5}}{\sqrt{7}}.$$

Accepted Answer

$$\frac{\sqrt{35}}{7}$$

Question 10

Add: $$\frac{9}{8} + \frac{5}{8}.$$

Accepted Answer

$$\frac{14}{8}$$

Question 11

What is the product of $$2 + 3\sqrt{5}$$ and its conjugate?

Accepted Answer

$$-59$$

Question 12

Multiply: $$\sqrt{2}\sqrt{6} + \sqrt{3}\sqrt{6}.$$

Accepted Answer

$$42 + 10\sqrt{5}$$

Question 13

Solve $$\sqrt{x-4} = 5.$$

Accepted Answer

$$x = 29$$

Question 14

Solve $$\sqrt{2x-7} = 1.$$

Accepted Answer

$$x = 4$$

Question 15

Find the distance and midpoint for $$(-6,4)$$ and $$(2,-4).$$

Accepted Answer

Distance: $$10\sqrt{2}$$, Midpoint: $$(-2,-1)$$

Question 16

Multiply and leave your answer in radical form: $$\sqrt{7}\sqrt{2}.$$

Accepted Answer

$$\sqrt{14}$$

Question 17

Multiply: $$p^3(p^2$ - 2p)$.

Accepted Answer

$$p^5$$ - $$2p^4$$

Question 18

Simplify $$y^{7/3}$$ \div $$y^{2/3}.$$

Accepted Answer

$$y^{5/3}$$

Question 19

Simplify $$\sqrt{75} - \sqrt{8}.$$

Accepted Answer

$$29\sqrt{2}$$

Intermediate Algebra Practice Test Guidance

Study Guide - Practice Questions