Chapter 10

Add or subtract as indicated. Write your answers in the form \(a+b i .\) $$ (8-3 i)+(-8+3 i) $$

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

Rationalize each denominator. Assume that all variables represent positive real numbers. \(\frac{1}{\sqrt{12 z}}\)

Use a calculator to approximate each square root to three decimal places. Check to see that each approximation is reasonable. $$ \sqrt{200} $$

Use radical notation to rewrite each expression. Simplify if possible. $$ (2 x)^{3 / 5} $$

Add or subtract as indicated. Assume that all variables represent positive real numbers. $$ -5 \sqrt[3]{625}+\sqrt[3]{40} $$

Use the quotient rule to simplify. Assume that all variables represent positive real numbers. $$ \sqrt[3]{\frac{2 x}{27 y^{12}}} $$

Add or subtract as indicated. Write your answers in the form \(a+b i .\) $$ 6-(8+4 i) $$

Solve. $$ \sqrt{5 x-4}=9 $$

Rationalize each denominator. Assume that all variables represent positive real numbers. \(\frac{1}{\sqrt{32 x}}\)

Use a calculator to approximate each square root to three decimal places. Check to see that each approximation is reasonable. $$ \sqrt{300} $$

Use radical notation to rewrite each expression. Simplify if possible. $$ 2 x^{3 / 5} $$

Add or subtract as indicated. Assume that all variables represent positive real numbers. $$ -2 \sqrt[3]{108}=\sqrt[3]{32} $$

Use the quotient rule to simplify. Assume that all variables represent positive real numbers. $$ \sqrt[3]{\frac{3 y}{8 x^{6}}} $$

Add or subtract as indicated. Write your answers in the form \(a+b i .\) $$ (9-4 i)-9 $$

Solve. $$ -\sqrt{2 x}+4=-6 $$

Rationalize each denominator. Assume that all variables represent positive real numbers. \(\frac{\sqrt[3]{2 y^{2}}}{\sqrt[3]{9 x^{2}}}\)

Find each cube root. $$ \sqrt[3]{64} $$

Use radical notation to rewrite each expression. Simplify if possible. $$ (7 x+2)^{2 / 3} $$

Add or subtract as indicated. Assume that all variables represent positive real numbers. $$ \sqrt{9 b^{3}}-\sqrt{25 b^{3}}+\sqrt{16 b^{3}} $$

Use the quotient rule to simplify. Assume that all variables represent positive real numbers. $$ \sqrt{\frac{x^{2} y}{169}} $$

Add or subtract as indicated. Write your answers in the form \(a+b i .\) $$ (6-3 i)-(4-2 i) $$

Solve. $$ -\sqrt{3 x+9}=-12 $$

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

Find each cube root. $$ \sqrt[3]{27} $$

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

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

Use the quotient rule to simplify. Assume that all variables represent positive real numbers. $$ \sqrt{\frac{y^{2} z}{225}} $$

Add or subtract as indicated. Write your answers in the form \(a+b i .\) $$ (-2-4 i)-(6-8 i) $$

Solve. $$ \sqrt{3 x+1}+2=0 $$

Rationalize each denominator. Assume that all variables represent positive real numbers. \(\sqrt[4]{\frac{16}{9 x^{7}}}\)

Find each cube root. $$ \sqrt[3]{\frac{1}{8}} $$v

Use radical notation to rewrite each expression. Simplify if possible. $$ \left(\frac{16}{9}\right)^{3 / 2} $$

Add or subtract as indicated. Assume that all variables represent positive real numbers. $$ 5 y \sqrt{8 y}+2 \sqrt{50 y^{3}} $$

Use the quotient rule to simplify. Assume that all variables represent positive real numbers. $$ \sqrt{\frac{5 x^{2}}{4 y^{2}}} $$

Add or subtract as indicated. Write your answers in the form \(a+b i .\) $$ (5-6 i)-4 i $$

Solve. $$ \sqrt{3 x+1}-2=0 $$

Rationalize each denominator. Assume that all variables represent positive real numbers. \(\sqrt[5]{\frac{32}{m^{6} n^{13}}}\)

Find each cube root. $$ \sqrt[3]{\frac{27}{64}} $$

Use radical notation to rewrite each expression. Simplify if possible. $$ \left(\frac{49}{25}\right)^{3 / 2} $$

Add or subtract as indicated. Assume that all variables represent positive real numbers. $$ 3 \sqrt{8 x^{2} y^{3}}-2 x \sqrt{32 y^{3}} $$

Use the quotient rule to simplify. Assume that all variables represent positive real numbers. $$ \sqrt{\frac{y^{10}}{9 x^{6}}} $$

Add or subtract as indicated. Write your answers in the form \(a+b i .\) $$ (6-2 i)+7 i $$

Solve. $$ \sqrt[4]{4 x+1}-2=0 $$

Rationalize each denominator. Assume that all variables represent positive real numbers. \(\frac{5 a}{\sqrt[5]{8 a^{9} b^{11}}}\)

Find each cube root. $$ \sqrt[3]{-1} $$

Write with positive exponents. Simplify if possible. $$ 8^{-4 / 3} $$

Add or subtract as indicated. Assume that all variables represent positive real numbers. $$ \sqrt[3]{54 x y^{3}}-5 \sqrt[3]{2 x y^{3}}+y \sqrt[3]{128 x} $$

Use the quotient rule to simplify. Assume that all variables represent positive real numbers. $$ -\sqrt[3]{\frac{z^{7}}{125 x^{3}}} $$

Add or subtract as indicated. Write your answers in the form \(a+b i .\) $$ (2+4 i)+(6-5 i) $$