$$f(21) = 4$$, \text{ domain: } [5, \infty)$

Question 1

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

Accepted Answer

$$2x\sqrt{3}$$

Question 2

Which of the following is the correct simplification of $$\sqrt{40}$$?

Accepted Answer

$$2\sqrt{10}$$

Question 3

Approximate $$\sqrt{17.309} to $$three decimal places.

Accepted Answer

$$4.163$$

Question 4

Simplify $$\sqrt{75x^2$y^3$$}$.

Accepted Answer

$$5xy\sqrt{3y}$$

Question 5

Given $$f(x) = \sqrt{x-5}$$, find $$f(21)$$ and state the domain.

Accepted Answer

$$f(21) = 4$$, 	ext{ domain: } [5, \infty)$

Question 6

Simplify $$\sqrt[3]{-8x^6$}.$$

Accepted Answer

$$-2x^2$$

Question 7

Rationalize the denominator: $$\frac{7b}{\sqrt{6}}.$$

Accepted Answer

$$\frac{7b\sqrt{6}}{6}$$

Question 8

Rationalize the denominator: $$\frac{\sqrt{5}}{2-\sqrt{3}}.$$

Accepted Answer

$$2\sqrt{5}+\sqrt{15}$$

Question 9

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

Accepted Answer

$$\frac{17}{5}$$

Question 10

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

Accepted Answer

$$-59$$

Question 11

Multiply: $$\sqrt{2}\sqrt{5}(\sqrt{3}-\sqrt{6}).$$

Accepted Answer

$$2\sqrt{15}-10\sqrt{5}$$

Question 12

Solve $$\sqrt{x-1} - 5 = 1.$$

Accepted Answer

$$36$$

Question 13

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

Accepted Answer

$$4$$

Question 14

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

Accepted Answer

$$10, (-3,-1)$$

Question 15

Multiply and leave your answer in radical form: $$\sqrt[3]{x^2$}\sqrt[3]{x^5$}.$$

Accepted Answer

$$x^{7/3}$$

Question 16

Multiply: $$y^{1/2}(y$$^{1/3}$$ - 2y$$^{1/6}$$)$.

Accepted Answer

$$y^{5/6}$$ - $$2y^{2/3}$$

Question 17

Simplify $$\sqrt[3]{y^3$}.$$

Accepted Answer

$$y$$

Question 18

Simplify $$5\sqrt{50} - 3\sqrt{18}.$$

Accepted Answer

$$29\sqrt{2}$$

Question 19

A chemist needs to mix a solution using $$\sqrt{75x^2$y^3$$}$$ grams of a compound. If x=2$ and y=3$, how many grams are needed?

Accepted Answer

$$30\sqrt{9}$$

Question 20

If the area of a square is $$50$$, what is the length of one side in simplest radical form?

Accepted Answer

$$5\sqrt{2}$$

Intermediate Algebra Practice Test 3 – Step-by-Step Study Guidance

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