Chapter 7

Add or subtract. $$ \frac{4 \sqrt{3}}{3}-\frac{\sqrt{12}}{3} $$

Find each root. Assume that all variables represent nonnegative real numbers. $$ \sqrt[4]{x^{20}} $$

Multiply. Write the product in the form \(a+b i .\) See Example 4. $$ 5 i(4-7 i) $$

Write with positive exponents. Simplify if possible. $$ y^{-1 / 6} $$

Solve. \(\sqrt[3]{x-4}-5=-7\)

Write the conjugate of each expression. $$ \sqrt{3}+y $$

Simplify. See Examples 3 and 4 $$ 3 \sqrt{8} $$

Add or subtract. $$ \frac{\sqrt{45}}{10}+\frac{7 \sqrt{5}}{10} $$

Find each root. Assume that all variables represent nonnegative real numbers. $$ \sqrt[6]{64 x^{12}} $$

Multiply. Write the product in the form \(a+b i .\) See Example 4. $$ (\sqrt{3}+2 i)(\sqrt{3}-2 i) $$

Write with positive exponents. Simplify if possible. $$ \frac{1}{a^{-2 / 3}} $$

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

Write the conjugate of each expression. $$ 5-\sqrt{a} $$

Simplify. See Examples 3 and 4 $$ \sqrt{24} $$

Add or subtract. $$ \frac{\sqrt[3]{8 x^{4}}}{7}+\frac{3 x \sqrt[3]{x}}{7} $$

Multiply. Write the product in the form \(a+b i .\) See Example 4. $$ (\sqrt{5}-5 i)(\sqrt{5}+5 i) $$

Write with positive exponents. Simplify if possible. $$ \frac{1}{n^{-k 9}} $$

Solve. \(\sqrt{3 y+6}=\sqrt{7 y-6}\)

Write the conjugate of each expression. $$ 6-\sqrt{b} $$

Simplify. See Examples 3 and 4 $$ \sqrt{20} $$

Add or subtract. $$ \frac{\sqrt[4]{48}}{5 x}-\frac{2 \sqrt[4]{3}}{10 x} $$

Find each root. Assume that all variables represent nonnegative real numbers. $$ \sqrt{81 x^{4}} $$

Multiply. Write the product in the form \(a+b i .\) See Example 4. $$ (4-2 i)^{2} $$

Write with positive exponents. Simplify if possible. $$ \frac{5}{7 x^{-3 / 4}} $$

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

Write the conjugate of each expression. $$ -7 \sqrt{5}+8 \sqrt{x} $$

Add or subtract. $$ \sqrt{\frac{28}{x^{2}}}+\sqrt{\frac{7}{4 x^{2}}} $$

Find each root. Assume that all variables represent nonnegative real numbers. $$ \sqrt[4]{81 x^{4}} $$

Multiply. Write the product in the form \(a+b i .\) See Example 4. $$ (6-3 i)^{2} $$

Write with positive exponents. Simplify if possible. $$ \frac{2}{3 y^{-5 / 7}} $$

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

Write the conjugate of each expression. $$ -9 \sqrt{2}-6 \sqrt{y} $$

Simplify. See Examples 3 and 4 $$ \sqrt{64 y^{9}} $$

Add or subtract. $$ \frac{\sqrt{99}}{5 x}-\sqrt{\frac{44}{x^{2}}} $$

Simplify. \(\sqrt{64 y^{9}}\)

Find each root. Assume that all variables represent nonnegative real numbers. $$ \sqrt[4]{256 x^{8}} $$

Solve. \(\sqrt[3]{-6 x-1}=\sqrt[3]{-2 x-5}\)

Write each quotient in the form \(a+b i .\) See Example 5. $$ \frac{4}{i} $$

Use the properties of exponents to simplify each expression. Write with positive exponents. $$ a^{2 / 3} a^{5 / 3} $$

Rationalize each denominator. See Example 4. $$ \frac{6}{2-\sqrt{7}} $$

Add or subtract. $$ \sqrt[3]{\frac{16}{27}}-\frac{\sqrt[3]{54}}{6} $$

Find each root. Assume that all variables represent nonnegative real numbers. $$ \sqrt{256 x^{8}} $$

Solve. \(\sqrt[3]{-4 x-3}=\sqrt[3]{-x-15}\)

Write each quotient in the form \(a+b i .\) See Example 5. $$ \frac{5}{6 i} $$

Use the properties of exponents to simplify each expression. Write with positive exponents. $$ b^{9 / 5} b^{8 / 5} $$

Rationalize each denominator. See Example 4. $$ \frac{3}{\sqrt{7}-4} $$

Simplify. See Examples 3 and 4 $$ \sqrt[3]{64 y^{9}} $$

Add or subtract. $$ \frac{\sqrt[3]{3}}{10}+\sqrt[3]{\frac{24}{125}} $$

Simplify. Assume that the variables represent any real number. $$ \sqrt{(-8)^{2}} $$

Solve. \(\sqrt{5 x-1}-\sqrt{x}+2=3\)