Chapter 10

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

Add or subtract as indicated. Assume that all variables represent positive real numbers. $$ 2 \sqrt[3]{3 a^{4}}-3 a \sqrt[3]{81 a} $$

Use the product rule to multiply. Assume that all variables represent positive real numbers. $$ \sqrt{3 y} \cdot \sqrt{5 x} $$

Write using i notation. $$ \sqrt{-63} $$

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

Rationalize each denominator. Assume that all variables represent positive real numbers. \(\frac{3}{\sqrt[3]{4 x^{2}}}\)

Find each square root. Assume that all variables represent nonnegative real numbers. $$ \sqrt{\frac{1}{4}} $$

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

Add or subtract as indicated. Assume that all variables represent positive real numbers. $$ \sqrt{9 b^{3}}-\sqrt{25 b^{3}}+\sqrt{49 b^{3}} $$

Use the product rule to multiply. Assume that all variables represent positive real numbers. $$ \sqrt{\frac{7}{x}} \cdot \sqrt{\frac{2}{y}} $$

Multiply or divide as indicated. $$ \sqrt{-2} \cdot \sqrt{-7} $$

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

Rationalize each denominator. Assume that all variables represent positive real numbers. \(\frac{5}{\sqrt[3]{3 y}}\)

Find each square root. Assume that all variables represent nonnegative real numbers. $$ \sqrt{\frac{9}{25}} $$

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

Add or subtract as indicated. Assume that all variables represent positive real numbers. $$ \sqrt{4 x^{7}}+9 x^{2} \sqrt{x^{3}}-5 x \sqrt{x^{5}} $$

Use the product rule to multiply. Assume that all variables represent positive real numbers. $$ \sqrt{\frac{6}{m}} \cdot \sqrt{\frac{n}{5}} $$

Multiply or divide as indicated. $$ \sqrt{-11} \cdot \sqrt{-3} $$

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

Rationalize each denominator. Assume that all variables represent positive real numbers. \(\frac{9}{\sqrt{3 a}}\)

Find each square root. Assume that all variables represent nonnegative real numbers. $$ \sqrt{0.0001} $$

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

Add or subtract as indicated. Assume that all variables represent positive real numbers. $$ \frac{5 \sqrt{2}}{3}+\frac{2 \sqrt{2}}{5} $$

Use the product rule to multiply. Assume that all variables represent positive real numbers. $$ \sqrt[4]{4 x^{3}} \cdot \sqrt[4]{5} $$

Multiply or divide as indicated. $$ \sqrt{-5} \cdot \sqrt{-10} $$

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

Rationalize each denominator. Assume that all variables represent positive real numbers. \(\frac{x}{\sqrt{5}}\)

Find each square root. Assume that all variables represent nonnegative real numbers. $$ \sqrt{0.04} $$

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

Add or subtract as indicated. Assume that all variables represent positive real numbers. $$ \frac{\sqrt{3}}{2}+\frac{4 \sqrt{3}}{3} $$

Use the product rule to multiply. Assume that all variables represent positive real numbers. $$ \sqrt[4]{a b^{2}} \cdot \sqrt[4]{27 a b} $$

Multiply or divide as indicated. $$ \sqrt{-2} \cdot \sqrt{-6} $$

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

Rationalize each denominator. Assume that all variables represent positive real numbers. \(\frac{3}{\sqrt[3]{2}}\)

Find each square root. Assume that all variables represent nonnegative real numbers. $$ -\sqrt{36} $$

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

Add or subtract as indicated. Assume that all variables represent positive real numbers. $$ \sqrt[3]{\frac{11}{8}}-\frac{\sqrt[3]{11}}{6} $$

Use the quotient rule to simplify. Assume that all variables represent positive real numbers. $$ \sqrt{\frac{6}{49}} $$

Multiply or divide as indicated. $$ \sqrt{16} \cdot \sqrt{-1} $$

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

Rationalize each denominator. Assume that all variables represent positive real numbers. \(\frac{5}{\sqrt[3]{9}}\)

Find each square root. Assume that all variables represent nonnegative real numbers. $$ -\sqrt{9} $$

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

Add or subtract as indicated. Assume that all variables represent positive real numbers. $$ \frac{2 \sqrt[3]{4}}{7}-\frac{\sqrt[3]{4}}{14} $$

Use the quotient rule to simplify. Assume that all variables represent positive real numbers. $$ \sqrt{\frac{10}{81}} $$

Multiply or divide as indicated. $$ \sqrt{3} \cdot \sqrt{-27} $$

Solve. $$ \sqrt{13-x}=x-1 $$

Rationalize each denominator. Assume that all variables represent positive real numbers. \(\frac{2 \sqrt{3}}{\sqrt{7}}\)

Find each square root. Assume that all variables represent nonnegative real numbers. $$ \sqrt{x^{10}} $$

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