# Precalculus: The Basics Radicals Review

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### True or False? A radical is an expression that uses a root, such as square root, cube root.

True
False
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### Evaluate the following equation:$$\sqrt{-512}$$

$$8$$
$$-8$$
$$-4$$
$$4$$
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### Evaluate the following equation:$$\sqrt{2\frac{10}{27}}$$

$$\frac{4}{3}$$
$$\frac{1}{3}$$
$$\frac{2}{3}$$
$$\frac{3}{4}$$
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### Simplify the following expression. Assume that $$x$$ is positive: $$\sqrt{8x^3}$$

$$x\sqrt{2x}$$
$$2x\sqrt{4x}$$
$$2x\sqrt{x}$$
$$2x\sqrt{2x}$$
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### Simplify the following expression. Assume that $$x$$ is positive. $$(\sqrt{x-2})(4\sqrt{x-2})$$

$$2x-2$$
$$4x-2$$
$$4x-1$$
$$x-2$$
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### Simplify the following expression. Assume that $$x$$ is positive. $$(2\sqrt{x}+1)(3-4\sqrt{x})$$

$$3+2\sqrt{x}-8x$$
$$1+2\sqrt{x}-8x$$
$$2+2\sqrt{x}-8x$$
$$3+3\sqrt{x}-8x$$
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### Simplify the following expression. Assume that $$a,b,c$$ is positive. $$\sqrt{54a^{6}b^{7}c^{2}}$$

$$3a^{2}b^{2}\sqrt{3bc^{2}}$$
$$3a^{2}b^{3}\sqrt{2bc^{2}}$$
$$a^{2}b^{2}\sqrt{2bc^{2}}$$
$$3a^{2}b^{2}\sqrt{2bc^{2}}$$
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### Multiply the following expression. Assume that $$x$$ is positive. $$\sqrt{x}(4-3\sqrt{x})$$

$$4\sqrt{x}-3x$$
$$4\sqrt{x}-x$$
$$4\sqrt{2x}-3x$$
$$2\sqrt{x}-3x$$
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### Rationalize the denominator. Assume that $$x$$ is positive. $$\frac{6}{\sqrt{x}}$$

$$\frac{2\sqrt{x}}{x}$$
$$\frac{6\sqrt{x}}{x}$$
$$\frac{2\sqrt{x}}{x}$$
$$\frac{7\sqrt{x}}{x}$$
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### Rationalize the denominator. Assume that $$x$$ and $$y$$ is positive. $$\frac{4}{\sqrt{x}+2\sqrt{y}}$$

$$\frac{4\sqrt{x}-8\sqrt{x}}{x-2y}$$
$$\frac{4\sqrt{x}-4\sqrt{x}}{x-4y}$$
$$\frac{4\sqrt{x}-8\sqrt{x}}{x-4y}$$
$$\frac{2\sqrt{x}-8\sqrt{x}}{x-4y}$$
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### Rationalize the denominator. Assume that $$x$$ is positive. $$\frac{\sqrt{x}-\sqrt{x-2}}{\sqrt{x}+\sqrt{x-2}}$$

$$x-\sqrt{x(x-3)}-1$$
$$x-\sqrt{x(x-2)}-2$$
$$x-\sqrt{x(x-3)}-2$$
$$x-\sqrt{x(x-2)}-1$$
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