Question 1

Which of the following is the correct list of the first 14 perfect squares?

Accepted Answer

$$1,\ 4,\ 9,\ 16,\ 25,\ 36,\ 49,\ 64,\ 81,\ 100,\ 121,\ 144,\ 169,\ 196$$

Question 2

Simplify $$\sqrt{192x^3$}.$$

Accepted Answer

$$8x\sqrt{3x}$$

Question 3

Simplify $$\dfrac{\sqrt{48x^3$}}{\sqrt{6x}}.$$

Accepted Answer

Question 4

Add: $$7\sqrt{3} + 12\sqrt{3}.$$

Accepted Answer

$$19\sqrt{3}$$

Question 5

Rationalize the denominator: $$\dfrac{7}{5 + \sqrt{3}}.$$

Accepted Answer

$$\dfrac{7(5 - \sqrt{3})}{25 - 3}$$

Question 6

Simplify $$5\sqrt{64}.$$

Accepted Answer

$$40$$

Question 7

Simplify $$2\sqrt[3]{27}.$$

Accepted Answer

$$6$$

Question 8

Simplify $$\sqrt{9x^3$}.$$

Accepted Answer

$$3x\sqrt{x}$$

Question 9

Simplify $$\sqrt{500}.$$

Accepted Answer

$$10\sqrt{5}$$

Question 10

Simplify $$\sqrt[3]{-125}.$$

Accepted Answer

$$-5$$

Question 11

Simplify $$(\sqrt[4]{5x}$$)^{1/2}$$ \cdot (\sqrt[4]{7x^3$}$$)^{3/4}$$.

Accepted Answer

$$\sqrt[8]{35x^4$}$$

Question 12

Simplify and rationalize the denominator: $$\sqrt{\dfrac{100}{9}}.$$

Accepted Answer

$$\dfrac{10}{3}$$

Question 13

Simplify $$\dfrac{\sqrt{150x^3$}}{2x}.$$

Accepted Answer

$$\dfrac{5\sqrt{6x}}{2}$$

Question 14

Simplify $$\dfrac{\sqrt{500x^3$}}{10x$$^{-1}$$}.$$

Accepted Answer

$$5x^2$$\sqrt{5}$$

Question 15

Add: $$8\sqrt{13} + 9\sqrt{13}.$$

Accepted Answer

$$17\sqrt{13}$$

Question 16

Simplify $$\sqrt[3]{8$$^{1/4}$$}.$$

Accepted Answer

$$2^{1/6}$$

Question 17

Simplify $$\dfrac{\sqrt[5]{32x^3$}}{\sqrt[4]{16x}}.$$

Accepted Answer

$$2^{3/20}x$$^{11/20}$

Question 18

A chemist needs to dilute a solution and uses the formula $$C = \sqrt{V}$$, where $$C is $$the concentration and $$V is $$the volume in liters. If the concentration must be $$5$$, what volume should the chemist use?

Accepted Answer

$$25$$ liters

Question 19

A biologist is studying the growth of bacteria, which doubles every hour. If the initial population is $$P_0$$, after $$t$$ hours, the population is $$P = P_0$ \cdot 2^t. If $$after $$3$$ hours the population is $$800$$, what was the initial population?

Accepted Answer

$$100$$

Precalculus Study Guide: Radicals and Rational Exponents (Section P.3)

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