Chapter 10

Solve. $$ \sqrt{7 x-4}=\sqrt{4-7 x} $$

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

Use the properties of exponents to simplify each expression. Write with positive exponents. $$ 5^{1 / 2} \cdot 5^{1 / 6} $$

Use the quotient rule to simplify. Assume that all variables represent positive real numbers. $$ \sqrt[3]{y^{5}} $$

Multiply. Write your answers in the form \(a+b i\). $$ (6-3 i)^{2} $$

Rationalize each numerator. Assume that all variables represent positive real numbers. \(\sqrt{\frac{18}{5}}\)

Solve. $$ \sqrt{3 x+4}-1=\sqrt{2 x+1} $$

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

Use the properties of exponents to simplify each expression. Write with positive exponents. $$ \frac{y^{1 / 3}}{y^{1 / 6}} $$

Multiply. Then simplify if possible. Assume that all variables represent positive real numbers. $$ \sqrt{7}(\sqrt{5}+\sqrt{3}) $$

Multiply. Write your answers in the form \(a+b i\). $$ (6-2 i)(3+i) $$

Rationalize each numerator. Assume that all variables represent positive real numbers. \(\sqrt{\frac{12}{7}}\)

Solve. $$ \sqrt{x-2}+3=\sqrt{4 x+1} $$

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

Use the properties of exponents to simplify each expression. Write with positive exponents. $$ \frac{x^{3 / 4}}{x^{1 / 8}} $$

Multiply. Then simplify if possible. Assume that all variables represent positive real numbers. $$ \sqrt{2}(\sqrt{15}-\sqrt{35}) $$

Multiply. Write your answers in the form \(a+b i\). $$ (2-4 i)(2-i) $$

Rationalize each numerator. Assume that all variables represent positive real numbers. \(\frac{\sqrt{4 x}}{7}\)

Solve. $$ \sqrt{y+3}-\sqrt{y-3}=1 $$

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

Use the properties of exponents to simplify each expression. Write with positive exponents. $$ \left(4 u^{2}\right)^{3 / 2} $$

Multiply. Then simplify if possible. Assume that all variables represent positive real numbers. $$ (\sqrt{5}-\sqrt{2})^{2} $$

Multiply. Write your answers in the form \(a+b i\). $$ (1-i)(1+i) $$

Rationalize each numerator. Assume that all variables represent positive real numbers. \(\frac{\sqrt{3 x^{5}}}{6}\)

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

Simplify. Assume that the variables represent any real number. $$ \sqrt{(-7)^{2}} $$

Use the properties of exponents to simplify each expression. Write with positive exponents. $$ \left(32^{1 / 5} x^{2 / 3}\right)^{3} $$

Multiply. Then simplify if possible. Assume that all variables represent positive real numbers. $$ (3 x-\sqrt{2})(3 x-\sqrt{2}) $$

Simplify. Assume that all variables represent positive real numbers. $$ \sqrt[5]{-243 z^{9}} $$

Multiply. Write your answers in the form \(a+b i\). $$ (6+2 i)(6-2 i) $$

Rationalize each numerator. Assume that all variables represent positive real numbers. \(\frac{\sqrt[3]{5 y^{2}}}{\sqrt[3]{4 x}}\)

Simplify. Assume that the variables represent any real number. $$ \sqrt[3]{(-8)^{3}} $$

Use the properties of exponents to simplify each expression. Write with positive exponents. $$ \frac{b^{1 / 2} b^{3 / 4}}{-b^{1 / 4}} $$

Multiply. Then simplify if possible. Assume that all variables represent positive real numbers. $$ \sqrt{3 x}(\sqrt{3}-\sqrt{x}) $$

Simplify. Assume that all variables represent positive real numbers. $$ \sqrt[3]{50 x^{14}} $$

Multiply. Write your answers in the form \(a+b i\). $$ (9+8 i)^{2} $$

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

Simplify. Assume that the variables represent any real number. $$ \sqrt[5]{(-7)^{5}} $$

Use the properties of exponents to simplify each expression. Write with positive exponents. $$ \frac{a^{1 / 4} a^{-1 / 2}}{a^{2 / 3}} $$

Multiply. Then simplify if possible. Assume that all variables represent positive real numbers. $$ \sqrt{5 y}(\sqrt{y}+\sqrt{5}) $$

Simplify. Assume that all variables represent positive real numbers. $$ \sqrt[3]{40 y^{10}} $$

Multiply. Write your answers in the form \(a+b i\). $$ (4+7 i)^{2} $$

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

Simplify. Assume that the variables represent any real number. $$ \sqrt{4 x^{2}} $$

Use the properties of exponents to simplify each expression. Write with positive exponents. $$ \frac{\left(x^{3}\right)^{1 / 2}}{x^{7 / 2}} $$

Multiply. Then simplify if possible. Assume that all variables represent positive real numbers. $$ (2 \sqrt{x}-5)(3 \sqrt{x}+1) $$

Simplify. Assume that all variables represent positive real numbers. $$ -\sqrt{32 a^{8} b^{7}} $$

Multiply. Write your answers in the form \(a+b i\). $$ (1-i)^{2} $$

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

Simplify. Assume that the variables represent any real number. $$ \sqrt[4]{16 x^{4}} $$