0. Review of Algebra

Simplify the radical.

$\(\sqrt{75}\)$

Simplify the radical.

$\(\sqrt{180}\)$

Simplify the radical.

$\(\sqrt{63x^2}\)$

True or False:

$\(\sqrt{9+16}\)$ and $\(\sqrt\)9+\(\sqrt{16}\)$ are equal.

Evaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √144+√25

Use the product rule to simplify the expressions in Exercises 13–22. In Exercises 17–22, assume that variables represent nonnegative real numbers. $\sqrt{2x^2}\cdot \sqrt{6x}$

Use the quotient rule to simplify the expressions in Exercises 23–32. Assume that x > 0. $\frac{\sqrt{150x^4}}{\sqrt{3x}}$

Use the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. √11 • √44

Use the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. ∛√4

Simplify each radical. Assume all variables represent positive real numbers. ∛(25 (-3)⁴ (5)³ )

Simplify each radical. Assume all variables represent positive real numbers. ⁶√√5³

Perform the indicated operations. Assume all variables represent positive real numbers. $3\(\sqrt\)[4]{x^5y} - 2x\(\sqrt\)[4]{xy}$

Perform the indicated operations. Assume all variables represent positive real numbers. (√3 + √8)²

Perform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. $\(\sqrt\)[4]{\(\frac{g^3h^5}{9r^6}\)}$