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# Radical Expressions and Equations

Combine your skills of working with exponents and manipulating expressions for radical glory.

# Radicals Warmup

What is the value of $$\sqrt{2} \times \sqrt{6} \times \sqrt{27}?$$

Simplify $$(\sqrt{x} + \sqrt{3})(\sqrt{x} - \sqrt{3})$$

$$\sqrt[2]{x} \times \sqrt[4]{x} \times \sqrt[6]{x} \times \sqrt[n]{x} = x$$ for all $$x > 0$$

What is the value of $$n?$$

$$f(x) = (\sqrt{x^{2} + a})(\sqrt{x^{2} - a})$$

For what value(s) of $$a$$ will the domain of $$f$$ be $$\mathbb{R}?$$

Simplify $$\sqrt[9]{x^{3}}$$

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