Chapter 7

Solve. \(x-\sqrt{4-3 x}=-8\)

Add or subtract. $$ \sqrt{16}-5 \sqrt{10}+7 $$

Use a calculator to approximate each square root to 3 decimal places. $$ \sqrt{300} $$

Use radical notation to write each expression. Simplify if possible. $$ 4^{5 / 2} $$

Rationalize each denominator. See Examples 1 through 3. $$ \frac{-5 \sqrt{2}}{\sqrt{11}} $$

Add or subtract. $$\sqrt{16}-5 \sqrt{10}+7$$

Solve. \(2 x+\sqrt{x+1}=8\)

Multiply or divide. See Example 2. $$ \sqrt{-11} \cdot \sqrt{-3} $$

Find each cube root. $$ \sqrt[3]{64} $$

Use radical notation to write each expression. Simplify if possible. $$ (-64)^{2 / 3} $$

Rationalize each denominator. See Examples 1 through 3. $$ \sqrt{\frac{2 x}{5 y}} $$

Solve. \(\sqrt{y+5}=2-\sqrt{y-4}\)

Add or subtract. $$ 2+3 \sqrt{y^{2}}-6 \sqrt{y^{2}}+5 $$

Find each cube root. $$ \sqrt[3]{27} $$

Use radical notation to write each expression. Simplify if possible. $$ (-8)^{4 / 3} $$

Solve. \(\sqrt{x+3}+\sqrt{x-5}=3\)

Use the quotient rule to simplify. See Examples 2 and 3 . $$ \sqrt[3]{\frac{3}{64}} $$

Add or subtract. $$ 3 \sqrt{7}-\sqrt[3]{x}+4 \sqrt{7}-3 \sqrt[3]{x} $$

Find each cube root. $$ \sqrt[3]{\frac{1}{8}} $$

Use radical notation to write each expression. Simplify if possible. $$ (-16)^{3 / 4} $$

Solve. \(\sqrt{x-3}+\sqrt{x+2}=5\)

Add or subtract. $$ 3 \sqrt{108}-2 \sqrt{18}-3 \sqrt{48} $$

Find each cube root. $$ \sqrt[3]{\frac{27}{64}} $$

Use radical notation to write each expression. Simplify if possible. $$ (-9)^{3 / 2} $$

Solve. \(\sqrt{2 x-4}-\sqrt{3 x+4}=-2\)

Add or subtract. $$ -\sqrt{75}+\sqrt{12}-3 \sqrt{3} $$

Find each cube root. $$ \sqrt[3]{-1} $$

Use radical notation to write each expression. Simplify if possible. $$ (2 x)^{3 / 5} $$

Solve. \(\sqrt{3 x-2}=5\)

Use the quotient rule to simplify. See Examples 2 and 3 . $$ \sqrt[3]{\frac{2 x}{81 y^{12}}} $$

Add or subtract. $$ -5 \sqrt[3]{625}+\sqrt[3]{40} $$

Find each cube root. $$ \sqrt[3]{-125} $$

Use radical notation to write each expression. Simplify if possible. $$ 2 x^{3 / 5} $$

Solve. \(\sqrt{5 x-4}=9\)

Rationalize each denominator. See Examples 1 through 3. $$ \sqrt{\frac{11 y}{45}} $$

Add or subtract. $$ -2 \sqrt[3]{108}-\sqrt[3]{32} $$

Find each cube root. $$ \sqrt[3]{x^{12}} $$

$$ \frac{\sqrt{-80}}{\sqrt{-10}} $$

Use radical notation to write each expression. Simplify if possible. $$ (7 x+2)^{2 / 3} $$

Solve. \(-\sqrt{2 x}+4=-6\)

Use the quotient rule to simplify. See Examples 2 and 3 . $$ \sqrt{\frac{x^{2} y}{100}} $$

Add or subtract. $$ a^{3} \sqrt{9 a b^{3}}-\sqrt{25 a^{7} b^{3}}+\sqrt{16 a^{7} b^{3}} $$

Rationalize each denominator. See Examples 1 through 3. $$ \frac{1}{\sqrt{12 z}} $$

Find each cube root. $$ \sqrt[3]{x^{15}} $$

Multiply or divide. See Example 2. $$ \frac{\sqrt{-40}}{\sqrt{-8}} $$

Use radical notation to write each expression. Simplify if possible. $$ (x-4)^{3 / 4} $$

Solve. \(-\sqrt{3 x+9}=-12\)

Rationalize each denominator. See Examples 1 through 3. $$ \frac{1}{\sqrt{32 x}} $$

Add or subtract. $$ \sqrt{4 x^{7} y^{5}}+9 x^{2} \sqrt{x^{3} y^{5}}-5 x y \sqrt{x^{5} y^{3}} $$

Find each cube root. $$ \sqrt[3]{-27 x^{9}} $$