Chapter 5

Solve each equation. Don't forget to check each of your potential solutions. \(\sqrt{x^{2}+5 x-20}=2\)

Find the following products and express answers in simplest radical form. All variables represent nonnegative real numbers. \(2 \sqrt{2}(3 \sqrt{12}-\sqrt{27})\)

Express each of the following in simplest radical form. All variables represent positive real numbers. \(\sqrt{96 a^{7} b^{8}}\)

Change each radical to simplest radical form. \(5 \sqrt{32}\)

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

Write each of the following in ordinary decimal notation. For example, \((3.18)(10)^{2}=318\). \((5.123)(10)^{-8}\)

For Problems \(31-44\), write each of the following in radical form. For example, \(3 x^{\frac{2}{3}}=3 \sqrt[3]{x^{2}}\) \(x^{\frac{4}{3}}\)

Solve each equation. Don't forget to check each of your potential solutions. \(\sqrt{x^{2}-x+1}=x+1\)

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

Express each of the following in simplest radical form. All variables represent positive real numbers. \(\sqrt{63 x^{6} y^{8}}\)

Change each radical to simplest radical form. \(-6 \sqrt{20}\)

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

Write each of the following in ordinary decimal notation. For example, \((3.18)(10)^{2}=318\). \((6)(10)^{-9}\)

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

Solve each equation. Don't forget to check each of your potential solutions. \(\sqrt{n^{2}-2 n-4}=n\)

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

Express each of the following in simplest radical form. All variables represent positive real numbers. \(\sqrt{28 x^{4} y^{12}}\)

Change each radical to simplest radical form. \(-4 \sqrt{54}\)

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

For Problems \(33-50\), use scientific notation and the properties of exponents to help you perform the following operations. \((0.0037)(0.00002)\)

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

Solve each equation. Don't forget to check each of your potential solutions. \(\sqrt{x^{2}+3 x+7}=x+2\)

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

Express each of the following in simplest radical form. All variables represent positive real numbers. \(2 \sqrt{40 a^{3}}\)

Change each radical to simplest radical form. \(\frac{2}{5} \sqrt{75}\)

Simplify each numerical expression. \(\frac{3^{3}}{3^{-1}}\)

Use scientific notation and the properties of exponents to help you perform the following operations. \((0.00003)(0.00025)\)

Write each of the following in radical form. For example, \(3 x^{\frac{2}{3}}=3 \sqrt[3]{x^{2}}\). \(5 x^{\frac{1}{4}}\)

Solve each equation. Don't forget to check each of your potential solutions. \(\sqrt{x^{2}+2 x+1}=x+3\)

Find the following products and express answers in simplest radical form. All variables represent nonnegative real numbers. \((\sqrt{7}-2)(\sqrt{7}-8)\)

Express each of the following in simplest radical form. All variables represent positive real numbers. \(4 \sqrt{90 a^{5}}\)

Change each radical to simplest radical form. \(\frac{1}{3} \sqrt{90}\)

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

Use scientific notation and the properties of exponents to help you perform the following operations. \((0.00007)(11,000)\)

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

Solve each equation. Don't forget to check each of your potential solutions. \(\sqrt{-4 x+17}=x-3\)

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

Express each of the following in simplest radical form. All variables represent positive real numbers. \(\frac{2}{3} \sqrt{96 x y^{3}}\)

Change each radical to simplest radical form. \(\frac{3}{2} \sqrt{24}\)

Simplify each numerical expression. \(\frac{10^{-2}}{10^{2}}\)

Use scientific notation and the properties of exponents to help you perform the following operations. \((0.000004)(120,000)\)

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

Solve each equation. Don't forget to check each of your potential solutions. \(\sqrt{2 x-1}=x-2\)

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

Express each of the following in simplest radical form. All variables represent positive real numbers. \(\frac{4}{5} \sqrt{125 x^{4} y}\)

Change each radical to simplest radical form. \(\frac{3}{4} \sqrt{45}\)

Simplify each numerical expression. \(\frac{10^{-2}}{10^{-5}}\)

Use scientific notation and the properties of exponents to help you perform the following operations. \(\frac{360,000,000}{0.0012}\)

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

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