91Ó°ÊÓ

Simplify each expression. Assume that all variables represent positive values. Assume no division by 0. SEE EXAMPLE 6. (OBJECTIVE 3) $$\frac{4 t^{2 / 3}}{8 t^{-2 / 5}}$$

Rationalize the denominator. All variables represent positive values. SEE EXAMPLE 11. (OBJECTIVE 4) $$\frac{\sqrt{3 y}+3}{\sqrt{3 y}-2}$$

Simplify each expression. All variables of square root expressions represent positive numbers. Assume no division by 0. $$\frac{1}{5} x^{5} y \sqrt{75 x^{3} y^{2}}$$

Rationalize the denominator. All variables represent positive values. SEE EXAMPLE 11. (OBJECTIVE 4) $$\frac{\sqrt{5 x}-1}{\sqrt{5 x}+2}$$

Find each square root. If it is not exact, give a decimal approximation correct to three decimal places. $$-\sqrt{625}$$

Simplify each radical expression. If the answer is not exact, round to the nearest hundredth. All variables represent positive values $$-\sqrt{729 x^{8} y^{2}}$$

Simplify. All variables represent positive values. $$3 \sqrt{72}+2 \sqrt{128}$$

Simplify each expression. Assume that all variables represent positive values. Assume no division by 0. SEE EXAMPLE 6. (OBJECTIVE 3) $$\frac{p^{3 / 4}}{p^{1 / 3}}$$

Simplify each expression. All variables of square root expressions represent positive numbers. Assume no division by 0. $$\sqrt{\frac{125}{121}}$$

Use a calculator to help solve each. Give any decimal answer rounded to the nearest tenth. The time \(t\) (in seconds) required for a pendulum to swing through one cycle is given by the formula \(t=1.11 \sqrt{L}\). Find the length \(L\) of a pendulum that completes one cycle in \(\frac{3}{2}\) seconds.