Practice Test

In the following exercises, simplify.

766.

$\sqrt{81 + 144}$

767.

$\sqrt{169 m^{4} n^{2}}$

768.

$\sqrt{36 n^{13}}$

769.

$3 \sqrt{13} + 5 \sqrt{2} + \sqrt{13}$

770.

$5 \sqrt{20} + 2 \sqrt{125}$

771.

$(3 \sqrt{6 y}) (2 \sqrt{50 y^{3}})$

772.

$(2 - 5 \sqrt{x}) (3 + \sqrt{x})$

773.

${(1 - 2 \sqrt{q})}^{2}$

774.

ⓐ $\sqrt[4]{a^{12}}$
ⓑ $\sqrt[3]{b^{21}}$

775.

ⓐ $\sqrt[4]{81 x^{12}}$
ⓑ $\sqrt[6]{64 y^{18}}$

776.

$\sqrt{\frac{64 r^{12}}{25 r^{6}}}$

777.

$\sqrt{\frac{14 y^{3}}{7 y}}$

778.

$\frac{\sqrt[5]{256 x^{7}}}{\sqrt[5]{4 x^{2}}}$

779.

$\sqrt[4]{512} - 2 \sqrt[4]{32}$

780.

ⓐ $256^{\frac{1}{4}}$
ⓑ $243^{\frac{1}{5}}$

781.

$49^{\frac{3}{2}}$

782.

$25^{- \frac{5}{2}}$

783.

$\frac{w^{\frac{3}{4}}}{w^{\frac{7}{4}}}$

784.

${(27 s^{\frac{3}{5}})}^{\frac{1}{3}}$

In the following exercises, rationalize the denominator.

785.

$\frac{3}{2 \sqrt{6}}$

786.

$\frac{\sqrt{3}}{\sqrt{x} + \sqrt{5}}$

In the following exercises, solve.

787.

$3 \sqrt{2 x - 3} - 20 = 7$

788.

$\sqrt{3 u - 2} = \sqrt{5 u + 1}$

In the following exercise, solve.

789.

A helicopter flying at an altitude of 600 feet dropped a package to a lifeboat. Use the formula $t = \frac{\sqrt{h}}{4}$ to find how many seconds it took for the package to reach the hiker. Round your answer to the nearest tenth of a second.