Practice Test

In the following exercises, simplify using absolute values as necessary.

579.

$\sqrt[3]{125 x^{9}}$

580.

$\sqrt{169 x^{8} y^{6}}$

581.

$\sqrt[3]{72 x^{8} y^{4}}$

582.

$\sqrt{\frac{45 x^{3} y^{4}}{180 x^{5} y^{2}}}$

In the following exercises, simplify. Assume all variables are positive.

583.

ⓐ $256^{- \frac{1}{4}}$ ⓑ $− 49^{\frac{3}{2}}$

584.

$\sqrt{−45}$

585.

$\frac{x^{- \frac{1}{4}} \cdot x^{\frac{5}{4}}}{x^{- \frac{3}{4}}}$

586.

${(\frac{8 x^{\frac{2}{3}} y^{- \frac{5}{2}}}{x^{- \frac{7}{3}} y^{\frac{1}{2}}})}^{\frac{1}{3}}$

587.

$\sqrt{48 x^{5}} - \sqrt{75 x^{5}}$

588.

$\sqrt{27 x^{2}} - 4 x \sqrt{12} + \sqrt{108 x^{2}}$

589.

$2 \sqrt{12 x^{5}} \cdot 3 \sqrt{6 x^{3}}$

590.

$\sqrt[3]{4} (\sqrt[3]{16} - \sqrt[3]{6})$

591.

$(4 - 3 \sqrt{3}) (5 + 2 \sqrt{3})$

592.

$\frac{\sqrt[3]{128}}{\sqrt[3]{54}}$

593.

$\frac{\sqrt{245 x y^{−4}}}{\sqrt{45 x^{−4} y^{3}}}$

594.

$\frac{1}{\sqrt[3]{5}}$

595.

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

596.

$\sqrt{−4} \cdot \sqrt{−9}$

597.

$−4 i (−2 - 3 i)$

598.

$\frac{4 + i}{3 - 2 i}$

599.

$i^{172}$

In the following exercises, solve.

600.

$\sqrt{2 x + 5} + 8 = 6$

601.

$\sqrt{x + 5} + 1 = x$

602.

$\sqrt[3]{2 x^{2} - 6 x - 23} = \sqrt[3]{x^{2} - 3 x + 5}$

In the following exercise, ⓐ find the domain of the function ⓑ graph the function ⓒ use the graph to determine the range.

603.

$g (x) = \sqrt{x + 2}$