Chapter 10

Solve. $$ \sqrt{2 x}=4 $$

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

Find the real square roots of each number. $$ 4 $$

Use radical notation to rewrite each expression. Simplify if possible. $$ 49^{1 / 2} $$

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

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

Write using i notation. $$ \sqrt{-24} $$

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

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

Find the real square roots of each number. $$ 9 $$

Use radical notation to rewrite each expression. Simplify if possible. $$ 64^{1 / 3} $$

Add or subtract as indicated. Assume that all variables represent positive real numbers. $$ \sqrt{27}-\sqrt{75} $$

Use the product rule to multiply. Assume that all variables represent positive real numbers. $$ \sqrt{11} \cdot \sqrt{10} $$

Write using i notation. $$ \sqrt{-32} $$

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

Rationalize each denominator. Assume that all variables represent positive real numbers. \(\sqrt{\frac{1}{5}}\)

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. $$ 2 \sqrt{2 x^{3}}+4 x \sqrt{8 x} $$

Use the product rule to multiply. Assume that all variables represent positive real numbers. $$ \sqrt[4]{8} \cdot \sqrt[4]{2} $$

Write using i notation. $$ -\sqrt{-36} $$

Solve. $$ \sqrt{x+1}=5 $$

Rationalize each denominator. Assume that all variables represent positive real numbers. \(\sqrt{\frac{1}{2}}\)

Use radical notation to rewrite each expression. Simplify if possible. $$ 8^{1 / 3} $$

Add or subtract as indicated. Assume that all variables represent positive real numbers. $$ 3 \sqrt{45 x^{3}}+x \sqrt{5 x} $$

Use the product rule to multiply. Assume that all variables represent positive real numbers. $$ \sqrt[4]{27} \cdot \sqrt[4]{3} $$

Write using i notation. $$ -\sqrt{-121} $$

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

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

Find the real square roots of each number. $$ 100 $$

Use radical notation to rewrite each expression. Simplify if possible. $$ \left(\frac{1}{16}\right)^{1 / 4} $$

Add or subtract as indicated. Assume that all variables represent positive real numbers. $$ 2 \sqrt{50}-3 \sqrt{125}+\sqrt{98} $$

Use the product rule to multiply. Assume that all variables represent positive real numbers. $$ \sqrt[3]{4} \cdot \sqrt[3]{9} $$

Write using i notation. $$ 8 \sqrt{-63} $$

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

Rationalize each denominator. Assume that all variables represent positive real numbers. \(\frac{6}{\sqrt[3]{9}}\)

Find the real square roots of each number. $$ 64 $$

Use radical notation to rewrite each expression. Simplify if possible. $$ \left(\frac{1}{64}\right)^{1 / 2} $$

Add or subtract as indicated. Assume that all variables represent positive real numbers. $$ 4 \sqrt{32}-\sqrt{18}+2 \sqrt{128} $$

Use the product rule to multiply. Assume that all variables represent positive real numbers. $$ \sqrt[3]{10} \cdot \sqrt[3]{5} $$

Write using i notation. $$ 4 \sqrt{-20} $$

Solve. $$ \sqrt{4 x-3}-5=0 $$

Rationalize each denominator. Assume that all variables represent positive real numbers. \(\frac{3}{\sqrt{8 x}}\)

Find each square root. Assume that all variables represent nonnegative real numbers. $$ \sqrt{100} $$

Use radical notation to rewrite each expression. Simplify if possible. $$ 169^{1 / 2} $$

Add or subtract as indicated. Assume that all variables represent positive real numbers. $$ \sqrt[3]{16 x}-\sqrt[3]{54 x} $$

Use the product rule to multiply. Assume that all variables represent positive real numbers. $$ \sqrt{2} \cdot \sqrt{3 x} $$

Write using i notation. $$ -\sqrt{54} $$

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

Rationalize each denominator. Assume that all variables represent positive real numbers. \(\frac{5}{\sqrt{27 a}}\)

Find each square root. Assume that all variables represent nonnegative real numbers. $$ \sqrt{400} $$