Chapter 5

Find the following products and express answers in simplest radical form. All variables represent nonnegative real numbers. \((2 \sqrt{6}+3 \sqrt{5})(\sqrt{8}-3 \sqrt{12})\)

Express each of the following in simplest radical form. All variables represent positive real numbers. \(\sqrt{\frac{2 x}{5 y}}\)

Change each radical to simplest radical form. \(-\frac{5}{6} \sqrt{28}\)

Simplify each numerical expression. \(2^{-2}+3^{-2}\)

Use scientific notation and the properties of exponents to help you perform the following operations. \(\frac{66,000,000,000}{0.022}\)

Write each of the following in radical form. For example, \(3 x^{\frac{2}{3}}=3 \sqrt[3]{x^{2}}\). \((5 x+y)^{\frac{1}{3}}\)

Solve each equation. Don't forget to check each of your potential solutions. \(\sqrt{n+6}=n+6\)

Find the following products and express answers in simplest radical form. All variables represent nonnegative real numbers. \((5 \sqrt{2}-4 \sqrt{6})(2 \sqrt{8}+\sqrt{6})\)

Express each of the following in simplest radical form. All variables represent positive real numbers. \(\sqrt{\frac{3 x}{2 y}}\)

Change each radical to simplest radical form. \(-\frac{2}{3} \sqrt{96}\)

Simplify each numerical expression. \(2^{-4}+5^{-1}\)

Use scientific notation and the properties of exponents to help you perform the following operations. \(\frac{0.000064}{16,000}\)

Write each of the following in radical form. For example, \(3 x^{\frac{2}{3}}=3 \sqrt[3]{x^{2}}\). \((2 a-3 b)^{\frac{2}{3}}\)

Solve each equation. Don't forget to check each of your potential solutions. \(\sqrt{3 y}=y-6\)

Find the following products and express answers in simplest radical form. All variables represent nonnegative real numbers. \((2 \sqrt{6}+5 \sqrt{5})(3 \sqrt{6}-\sqrt{5})\)

Express each of the following in simplest radical form. All variables represent positive real numbers. \(\sqrt{\frac{5}{12 x^{4}}}\)

Change each radical to simplest radical form. \(\sqrt{\frac{19}{4}}\)

Simplify each numerical expression. \(\left(\frac{1}{3}\right)^{-1}-\left(\frac{2}{5}\right)^{-1}\)

Use scientific notation and the properties of exponents to help you perform the following operations. \(\frac{0.00072}{0.0000024}\)

Write each of the following in radical form. For example, \(3 x^{\frac{2}{3}}=3 \sqrt[3]{x^{2}}\). \((5 a+7 b)^{\frac{3}{5}}\)

Solve each equation. Don't forget to check each of your potential solutions. \(2 \sqrt{n}=n-3\)

Find the following products and express answers in simplest radical form. All variables represent nonnegative real numbers. \((7 \sqrt{3}-\sqrt{7})(2 \sqrt{3}+4 \sqrt{7})\)

Express each of the following in simplest radical form. All variables represent positive real numbers. \(\sqrt{\frac{7}{8 x^{2}}}\)

Change each radical to simplest radical form. \(\sqrt{\frac{22}{9}}\)

Simplify each numerical expression. \(\left(\frac{3}{2}\right)^{-1}-\left(\frac{1}{4}\right)^{-1}\)

Use scientific notation and the properties of exponents to help you perform the following operations. \(\frac{(60,000)(0.006)}{(0.0009)(400)}\)

Write each of the following in radical form. For example, \(3 x^{\frac{2}{3}}=3 \sqrt[3]{x^{2}}\). \(x^{\frac{2}{3}} y^{\frac{1}{3}}\)

Solve each equation. Don't forget to check each of your potential solutions. \(4 \sqrt{x}+5=x\)

Find the following products and express answers in simplest radical form. All variables represent nonnegative real numbers. \((3 \sqrt{2}-5 \sqrt{3})(6 \sqrt{2}-7 \sqrt{3})\)

Express each of the following in simplest radical form. All variables represent positive real numbers. \(\frac{5}{\sqrt{18 y}}\)

Change each radical to simplest radical form. \(\sqrt{\frac{27}{16}}\)

Simplify each numerical expression. \(\left(2^{-3}+3^{-2}\right)^{-1}\)

Use scientific notation and the properties of exponents to help you perform the following operations. \(\frac{(0.00063)(960,000)}{(3,200)(0.0000021)}\)

Write each of the following in radical form. For example, \(3 x^{\frac{2}{3}}=3 \sqrt[3]{x^{2}}\). \(x^{\frac{3}{7}} y^{\frac{5}{7}}\)

Solve each equation. Don't forget to check each of your potential solutions. \(\sqrt{-x}-6=x\)

Find the following products and express answers in simplest radical form. All variables represent nonnegative real numbers. \((\sqrt{8}-3 \sqrt{10})(2 \sqrt{8}-6 \sqrt{10})\)

Express each of the following in simplest radical form. All variables represent positive real numbers. \(\frac{3}{\sqrt{12 x}}\)

Change each radical to simplest radical form. \(\sqrt{\frac{8}{25}}\)

Simplify each numerical expression. \(\left(5^{-1}-2^{-3}\right)^{-1}\)

Use scientific notation and the properties of exponents to help you perform the following operations. \(\frac{(0.0045)(60,000)}{(1800)(0.00015)}\)

Write each of the following in radical form. For example, \(3 x^{\frac{2}{3}}=3 \sqrt[3]{x^{2}}\). \(-3 x^{\frac{1}{5}} y^{\frac{2}{5}}\)

Solve each equation. Don't forget to check each of your potential solutions. \(\sqrt[3]{x-2}=3\)

Find the following products and express answers in simplest radical form. All variables represent nonnegative real numbers. \((\sqrt{6}+4)(\sqrt{6}-4)\)

Express each of the following in simplest radical form. All variables represent positive real numbers. \(\frac{\sqrt{7 x}}{\sqrt{8 y^{5}}}\)

Change each radical to simplest radical form. \(\sqrt{\frac{75}{81}}\)

For Problems \(43-62\), simplify each expression. Express final results without using zero or negative integers as exponents. \(x^{2} \cdot x^{-8}\)

Use scientific notation and the properties of exponents to help you perform the following operations. \(\frac{(0.00016)(300)(0.028)}{0.064}\)

Write each of the following in radical form. For example, \(3 x^{\frac{2}{3}}=3 \sqrt[3]{x^{2}}\). \(-4 x^{\frac{3}{4}} y^{\frac{1}{4}}\)

Solve each equation. Don't forget to check each of your potential solutions. \(\sqrt[3]{x+1}=4\)

Find the following products and express answers in simplest radical form. All variables represent nonnegative real numbers. \((\sqrt{7}-2)(\sqrt{7}+2)\)