Chapter 7

Simplify. Assume that variables represent positive real numbers. $$ \sqrt{100} $$

Use radical notation to write each expression. Simplify if possible. $$ 49^{1 / 2} $$

Simplify. See Example 1. $$ \sqrt{-81} $$

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

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

Add or subtract. $$\sqrt{8}-\sqrt{32}$$

Rationalize each denominator. See Examples I through 3. \(\frac{\sqrt{2}}{\sqrt{7}}\)

Simplify. Assume that variables represent positive real numbers. $$ \sqrt{400} $$

Use radical notation to write each expression. Simplify if possible. $$ 64^{1 / 3} $$

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

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

Use the product rule to multiply. See Example \(I\). \(\sqrt{11} \cdot \sqrt{10}\)

Add or subtract. $$ \sqrt{27}-\sqrt{75} $$

Simplify. See Example 1. $$ \sqrt{-49} $$

Simplify. Assume that variables represent positive real numbers. $$ \sqrt{\frac{1}{4}} $$

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

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

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

Use the product rule to multiply. See Example \(I\). \(\sqrt[4]{8} \cdot \sqrt[4]{2}\)

Add or subtract. $$ 2 \sqrt{2 x^{3}}+4 x \sqrt{8 x} $$

Simplify. Assume that variables represent positive real numbers. $$ \sqrt{\frac{9}{25}} $$

Use radical notation to write each expression. Simplify if possible. $$ 8^{1 / 3} $$

Simplify. See Example 1. $$ \sqrt{-3} $$

Solve. \(\sqrt{x+1}=5\)

Add or subtract. $$ 3 \sqrt{45 x^{3}}+x \sqrt{5 x} $$

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

Use the product rule to multiply. See Example \(I\). \(\sqrt[4]{27} \cdot \sqrt[4]{3}\)

Simplify. Assume that variables represent positive real numbers. $$ \sqrt{0.0001} $$

Use radical notation to write each expression. Simplify if possible. $$ \left(\frac{1}{16}\right)^{1 / 4} $$

Simplify. See Example 1. $$ -\sqrt{16} $$

Use the product rule to multiply. See Example \(I\). \(\sqrt[3]{4} \cdot \sqrt[3]{9}\)

Add or subtract. $$ 2 \sqrt{50}-3 \sqrt{125}+\sqrt{98} $$

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

Simplify. Assume that variables represent positive real numbers. $$ \sqrt{0.04} $$

Use radical notation to write each expression. Simplify if possible. $$ \left(\frac{1}{64}\right)^{1 / 2} $$

Simplify. See Example 1. $$ -\sqrt{4} $$

Rationalize each denominator. See Examples 1 through 3. $$ \sqrt{\frac{25}{y}} $$

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

Use the product rule to multiply. See Example \(I\). \(\sqrt[3]{10} \cdot \sqrt[3]{5}\)

Add or subtract. $$ 4 \sqrt{32}-\sqrt{18}+2 \sqrt{128} $$

Simplify. Assume that variables represent positive real numbers. $$ -\sqrt{36} $$

Use radical notation to write each expression. Simplify if possible. $$ 169^{1 / 2} $$

Simplify. See Example 1. $$ \sqrt{-64} $$

Rationalize each denominator. See Examples 1 through 3. $$ \frac{4}{\sqrt{3}} $$

Solve. \(\sqrt{4 x-3}-5=0\)

Add or subtract. $$ \sqrt[3]{16 x}-\sqrt[3]{54 x} $$

Simplify. Assume that variables represent positive real numbers. $$ -\sqrt{9} $$

Use radical notation to write each expression. Simplify if possible. $$ 81^{1 / 4} $$

Rationalize each denominator. See Examples 1 through 3. $$ \frac{6}{\sqrt[3]{9}} $$

Solve. \(\sqrt{x-3}-1=0\)