Chapter 5

Multiply and simplify where possible. \((-5 \sqrt{8})(-6 \sqrt{7})\)

Use the distributive property to help simplify each of the following. \(6 \sqrt{12}+\sqrt{3}-2 \sqrt{48}\)

Evaluate each of the following. For example, \(\sqrt{25}=5\). \(\sqrt[3]{-125}\)

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

Write each of the following in scientific notation. For example \(27800=(2.78)(10)^{4}\). \(376.4\)

Evaluate each numerical expression. \(36^{-\frac{1}{2}}\)

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

Multiply and simplify where possible. \((5 \sqrt{6})(4 \sqrt{6})\)

Use the distributive property to help simplify each of the following. \(-9 \sqrt{24}+3 \sqrt{54}-12 \sqrt{6}\)

Evaluate each of the following. For example, \(\sqrt{25}=5\). \(\sqrt[4]{81}\)

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

Write each of the following in scientific notation. For example \(27800=(2.78)(10)^{4}\). \(9126.21\)

Evaluate each numerical expression. \(81^{-\frac{1}{2}}\)

Solve each equation. Don't forget to check each of your potential solutions. \(\sqrt{2 y-3}=5\)

For Problems \(1-14\), multiply and simplify where possible. \((3 \sqrt{7})(2 \sqrt{7})\)

Use the distributive property to help simplify each of the following. \(13 \sqrt{28}-2 \sqrt{63}-7 \sqrt{7}\)

Evaluate each of the following. For example, \(\sqrt{25}=5\). \(-\sqrt[4]{16}\)

Simplify each numerical expression. \(\left(\frac{2}{7}\right)^{-2}\)

Write each of the following in scientific notation. For example \(27800=(2.78)(10)^{4}\). \(0.347\)

Evaluate each numerical expression. \(\left(\frac{1}{27}\right)^{-\frac{1}{3}}\)

Solve each equation. Don't forget to check each of your potential solutions. \(\sqrt{4 y-3}-6=0\)

Multiply and simplify where possible. \((2 \sqrt[3]{4})(6 \sqrt[3]{2})\)

Use the distributive property to help simplify each of the following. \(\frac{3}{4} \sqrt{7}-\frac{2}{3} \sqrt{28}\)

Evaluate each of the following. For example, \(\sqrt{25}=5\). \(\sqrt{\frac{16}{25}}\)

Simplify each numerical expression. \(\left(-\frac{3}{4}\right)^{0}\)

Write each of the following in scientific notation. For example \(27800=(2.78)(10)^{4}\). \(0.2165\)

Evaluate each numerical expression. \(\left(-\frac{8}{27}\right)^{-\frac{1}{3}}\)

Solve each equation. Don't forget to check each of your potential solutions. \(\sqrt{3 y+5}-2=0\)

Multiply and simplify where possible. \((4 \sqrt[3]{3})(5 \sqrt[3]{9})\)

Use the distributive property to help simplify each of the following. \(\frac{3}{5} \sqrt{5}-\frac{1}{4} \sqrt{80}\)

Evaluate each of the following. For example, \(\sqrt{25}=5\). \(\sqrt{\frac{25}{64}}\)

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

Write each of the following in scientific notation. For example \(27800=(2.78)(10)^{4}\). \(0.0214\)

Evaluate each numerical expression. \(4^{\frac{3}{2}}\)

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

Multiply and simplify where possible. \((4 \sqrt[3]{6})(7 \sqrt[3]{4})\)

Use the distributive property to help simplify each of the following. \(\frac{3}{5} \sqrt{40}+\frac{5}{6} \sqrt{90}\)

Evaluate each of the following. For example, \(\sqrt{25}=5\). \(-\sqrt{\frac{36}{49}}\)

Simplify each numerical expression. \(\frac{1}{\left(\frac{3}{7}\right)^{-2}}\)

Write each of the following in scientific notation. For example \(27800=(2.78)(10)^{4}\). \(0.0037\)

Evaluate each numerical expression. \(64^{\frac{2}{3}}\)

Solve each equation. Don't forget to check each of your potential solutions. \(\sqrt{4 x-1}-3=2\)

Multiply and simplify where possible. \((9 \sqrt[3]{6})(2 \sqrt[3]{9})\)

Use the distributive property to help simplify each of the following. \(\frac{3}{8} \sqrt{96}-\frac{2}{3} \sqrt{54}\)

Evaluate each of the following. For example, \(\sqrt{25}=5\). \(\sqrt{\frac{16}{64}}\)

Simplify each numerical expression. \(-\left(\frac{5}{6}\right)^{0}\)

Write each of the following in scientific notation. For example \(27800=(2.78)(10)^{4}\). \(0.00005\)

Evaluate each numerical expression. \(27^{\frac{4}{3}}\)

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

For Problems \(15-52\), find the following products and express answers in simplest radical form. All variables represent nonnegative real numbers. \(\sqrt{2}(\sqrt{3}+\sqrt{5})\)