Chapter 7

Use the product rule to multiply. See Example \(I\). \(\sqrt{3 y} \cdot \sqrt{5 x}\)

Add or subtract. $$ 2 \sqrt[3]{3 a^{4}}-3 a \sqrt[3]{81 a} $$

Simplify. Assume that variables represent positive real numbers. $$ \sqrt{x^{10}} $$

Use radical notation to write each expression. Simplify if possible. $$ 2 m^{1 / 3} $$

Rationalize each denominator. See Examples 1 through 3. $$ \frac{3}{\sqrt{8 x}} $$

Solve. \(\sqrt{2 x-3}-2=1\)

Use the product rule to multiply. See Example \(I\). \(\sqrt{\frac{7}{x}} \cdot \sqrt{\frac{2}{y}}\)

Add or subtract. $$ \sqrt{9 b^{3}}-\sqrt{25 b^{3}}+\sqrt{49 b^{3}} $$

Simplify. Assume that variables represent positive real numbers. $$ \sqrt{x^{16}} $$

Use radical notation to write each expression. Simplify if possible. $$ (2 m)^{1 / 3} $$

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

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

Rationalize each denominator. See Examples 1 through 3. $$ \frac{5}{\sqrt{27 a}} $$

Use the product rule to multiply. See Example \(I\). $$ \sqrt{\frac{6}{m}} \cdot \sqrt{\frac{n}{5}} $$

Simplify. Assume that variables represent positive real numbers. $$ \sqrt{16 y^{6}} $$

Use radical notation to write each expression. Simplify if possible. $$ \left(9 x^{4}\right)^{1 / 2} $$

Solve. \(\sqrt[3]{6 x}=-3\)

Use the product rule to multiply. See Example \(I\). $$ \sqrt[4]{4 x^{3}} \cdot \sqrt[4]{5} $$

Add or subtract. $$ \frac{5 \sqrt{2}}{3}+\frac{2 \sqrt{2}}{5} $$

Simplify. Assume that variables represent positive real numbers. $$ \sqrt{64 y^{20}} $$

Use radical notation to write each expression. Simplify if possible. $$ \left(16 x^{8}\right)^{1 / 2} $$

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

Use the product rule to multiply. See Example \(I\). $$ \sqrt[4]{a b^{2}} \cdot \sqrt[4]{27 a b} $$

Add or subtract. $$ \frac{\sqrt{3}}{2}+\frac{4 \sqrt{3}}{3} $$

Use a calculator to approximate each square root to 3 decimal places. $$ \sqrt{7} $$

Use radical notation to write each expression. Simplify if possible. $$ (-27)^{1 / 3} $$

Solve. \(\sqrt[3]{x-2}-3=0\)

Use the quotient rule to simplify. See Examples 2 and 3 . $$ \sqrt{\frac{6}{49}} $$

Add or subtract. $$ \sqrt[3]{\frac{11}{8}}-\frac{\sqrt[3]{11}}{6} $$

Use a calculator to approximate each square root to 3 decimal places. $$ \sqrt{11} $$

Use radical notation to write each expression. Simplify if possible. $$ -64^{1 / 2} $$

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

Solve. \(\sqrt[3]{2 x-6}-4=0\)

Add or subtract. $$ \frac{2 \sqrt[3]{4}}{7}-\frac{\sqrt[3]{4}}{14} $$

Use a calculator to approximate each square root to 3 decimal places. $$ \sqrt{38} $$

Simplify. See Example 1. $$ -\sqrt{54} $$

Use radical notation to write each expression. Simplify if possible. $$ -16^{1 / 4} $$

Rationalize each denominator. See Examples 1 through 3. $$ \frac{3}{\sqrt[3]{2}} $$

Solve. \(\sqrt{13-x}=x-1\)

Add or subtract. $$ \frac{\sqrt{20 x}}{9}+\sqrt{\frac{5 x}{9}} $$

Use the quotient rule to simplify. See Examples 2 and 3 . $$ \sqrt{\frac{2}{49}} $$

Use a calculator to approximate each square root to 3 decimal places. $$ \sqrt{56} $$

Simplify. See Example 1. $$ \sqrt{-63} $$

Use radical notation to write each expression. Simplify if possible. $$ (-32)^{1 / 5} $$

Rationalize each denominator. See Examples 1 through 3. $$ \frac{5}{\sqrt[3]{9}} $$

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

Add or subtract. $$ \frac{3 x \sqrt{7}}{5}+\sqrt{\frac{7 x^{2}}{100}} $$

Use a calculator to approximate each square root to 3 decimal places. $$ \sqrt{200} $$

Use radical notation to write each expression. Simplify if possible. $$ 16^{34} $$

Rationalize each denominator. See Examples 1 through 3. $$ \frac{2 \sqrt{3}}{\sqrt{7}} $$