Algebra
# Radical Expressions and Equations

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