Question 1

Which of the following is equivalent to $$\sqrt[3]{x^6$}$$ for all real $$x$$?

Accepted Answer

$$|x^2$|$$

Question 2

Simplify the expression $$\sqrt{50} + 2\sqrt{8}.$$

Accepted Answer

$$7\sqrt{2}$$

Question 3

A spaceship travels at a speed where time dilation is given by $$t = \dfrac{t_0$}{\sqrt{1 - v^2$/c^2$$}}$$. If v = 0.6c$, what is $$\sqrt{1 - $$v^2/c^2$}$$?

Accepted Answer

$$0.8$$

Question 4

Which of the following is the simplified form of $$\dfrac{\sqrt{18}}{\sqrt{2}}$$?

Accepted Answer

$$3$$

Question 5

Rationalize the denominator of $$\dfrac{5}{2\sqrt{3}}.$$

Accepted Answer

$$\dfrac{5\sqrt{3}}{6}$$

Question 6

Simplify $$\sqrt{12x^4$}$$ for $$x \geq 0.$$

Accepted Answer

$$2x^2$$\sqrt{3}$$

Question 7

Which of the following is equivalent to $$16^{3/4}$$?

Accepted Answer

Question 8

Simplify $$\sqrt{2x} \cdot \sqrt{8x^3$}$$ for $$x \geq 0.$$

Accepted Answer

$$4x^2$$

Question 9

Which of the following is the correct simplification of $$\sqrt{\dfrac{49}{16}}$$?

Accepted Answer

$$\dfrac{7}{4}$$

Question 10

Simplify $$\$$left(27x^6$$\$$right)^{1/3}$$ for x$$ \geq 0$$.

Accepted Answer

$$3x^2$$

Question 11

Add: $$3\sqrt{5} + 2\sqrt{20}.$$

Accepted Answer

$$7\sqrt{5}$$

Question 12

Which of the following is equivalent to $$x^{2/5}$$ \cdot $$x^{3/5}$$?

Accepted Answer

$$x$$

Question 13

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

Accepted Answer

$$\dfrac{7\sqrt{5}}{5}$$

Question 14

Simplify $$\sqrt[4]{81x^8$}$$ for $$x \geq 0.$$

Accepted Answer

$$3x^2$$

Question 15

Which of the following is equivalent to $$\left(\dfrac{1}{8}\$$right)^{-2/3}$$?

Accepted Answer

$$4$$

Question 16

Subtract: $$5\sqrt{3} - 2\sqrt{12}.$$

Accepted Answer

$$1\sqrt{3}$$

Question 17

Simplify $$\sqrt{45x^2$y^4$$}$$ for x$$ \geq 0$$, y$$ \geq 0$.

Accepted Answer

$$3y^2x$$\sqrt{5}$$

Question 18

Which of the following is equivalent to $$\sqrt[3]{-27x^6$}$$ for all real $$x$$?

Accepted Answer

$$-3x^2$$

Question 19

Simplify $$\left(\sqrt{5} - \sqrt{2}\right)\left(\sqrt{5} + \sqrt{2}\right).$$

Accepted Answer

$$3$$

Question 20

If $$a \u003e 0$$ and $$b \u003e 0$$, which of the following is equivalent to $$\dfrac{\sqrt{a}}{\sqrt{b}}$$?

Accepted Answer

$$\sqrt{\dfrac{a}{b}}$$

Precalculus Study Guide: Radicals and Rational Exponents

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