Chapter 10

Add or subtract as indicated. Assume that all variables represent positive real numbers. $$ \frac{\sqrt{20 x}}{9}+\sqrt{\frac{5 x}{9}} $$

Use the quotient rule to simplify. Assume that all variables represent positive real numbers. $$ \sqrt{\frac{2}{49}} $$

Multiply or divide as indicated. $$ \frac{\sqrt{-9}}{\sqrt{3}} $$

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

Rationalize each denominator. Assume that all variables represent positive real numbers. \(\frac{-5 \sqrt{2}}{\sqrt{11}}\)

Find each square root. Assume that all variables represent nonnegative real numbers. $$ \sqrt{x^{16}} $$

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

Add or subtract as indicated. Assume that all variables represent positive real numbers. $$ \frac{3 x \sqrt{7}}{5}+\sqrt{\frac{7 x^{2}}{100}} $$

Use the quotient rule to simplify. Assume that all variables represent positive real numbers. $$ \sqrt{\frac{5}{121}} $$

Multiply or divide as indicated. $$ \frac{\sqrt{49}}{\sqrt{-10}} $$

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

Rationalize each denominator. Assume that all variables represent positive real numbers. \(\sqrt{\frac{2 x}{5 y}}\)

Find each square root. Assume that all variables represent nonnegative real numbers. $$ \sqrt{16 y^{6}} $$

Use radical notation to rewrite each expression. Simplify if possible. $$ 16^{3 / 4} $$

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

Use the quotient rule to simplify. Assume that all variables represent positive real numbers. $$ \sqrt[4]{\frac{x^{3}}{16}} $$

Multiply or divide as indicated. $$ \frac{\sqrt{-80}}{\sqrt{-10}} $$

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

Rationalize each denominator. Assume that all variables represent positive real numbers. \(\sqrt{\frac{13 a}{2 b}}\)

Find each square root. Assume that all variables represent nonnegative real numbers. $$ \sqrt{64 y^{20}} $$

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

Add or subtract as indicated. Assume that all variables represent positive real numbers. $$ \sqrt{16}-5 \sqrt{10}+7 $$

Use the quotient rule to simplify. Assume that all variables represent positive real numbers. $$ \sqrt[4]{\frac{y}{81 x^{4}}} $$

Solve. $$ \sqrt{y+5}=2+\sqrt{y-2} $$

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

Use a calculator to approximate each square root to three decimal places. Check to see that each approximation is reasonable. $$ \sqrt{7} $$

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

Add or subtract as indicated. Assume that all variables represent positive real numbers. $$ 2+3 \sqrt{y^{2}}-6 \sqrt{y^{2}}+5 $$

Use the quotient rule to simplify. Assume that all variables represent positive real numbers. $$ \sqrt[3]{\frac{4}{27}} $$

Add or subtract as indicated. Write your answers in the form \(a+b i .\) $$ (4-7 i)+(2+3 i) $$

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

Rationalize each denominator. Assume that all variables represent positive real numbers. \(\sqrt[3]{\frac{7}{10}}\)

Use a calculator to approximate each square root to three decimal places. Check to see that each approximation is reasonable. $$ \sqrt{11} $$

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

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

Use the quotient rule to simplify. Assume that all variables represent positive real numbers. $$ \sqrt[3]{\frac{3}{64}} $$

Add or subtract as indicated. Write your answers in the form \(a+b i .\) $$ (2-4 i)-(2-i) $$

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

Rationalize each denominator. Assume that all variables represent positive real numbers. \(\sqrt{\frac{3 x}{50}}\)

Use a calculator to approximate each square root to three decimal places. Check to see that each approximation is reasonable. $$ \sqrt{38} $$

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

Add or subtract as indicated. Assume that all variables represent positive real numbers. $$ 3 \sqrt{108}-2 \sqrt{18}-3 \sqrt{48} $$

Use the quotient rule to simplify. Assume that all variables represent positive real numbers. $$ \sqrt[4]{\frac{8}{x^{8}}} $$

Add or subtract as indicated. Write your answers in the form \(a+b i .\) $$ (6+5 i)-(8-i) $$

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

Rationalize each denominator. Assume that all variables represent positive real numbers. \(\sqrt{\frac{11 y}{45}}\)

Use a calculator to approximate each square root to three decimal places. Check to see that each approximation is reasonable. $$ \sqrt{56} $$

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

Add or subtract as indicated. Assume that all variables represent positive real numbers. $$ -\sqrt{75}+\sqrt{12}-3 \sqrt{3} $$

Use the quotient rule to simplify. Assume that all variables represent positive real numbers. $$ \sqrt[4]{\frac{a^{3}}{81}} $$