Chapter 5

Use the distributive property to help simplify each of the following. \(\frac{3 \sqrt{18}}{5}-\frac{5 \sqrt{72}}{6}+\frac{3 \sqrt{98}}{4}\)

Evaluate each of the following. For example, \(\sqrt{25}=5\). \(\sqrt{\frac{9}{36}}\)

Simplify each numerical expression. \(2^{7} \cdot 2^{-3}\)

Write each of the following in scientific notation. For example \(27800=(2.78)(10)^{4}\). \(0.00000082\)

Evaluate each numerical expression. \(4^{\frac{7}{2}}\)

Solve each equation. Don't forget to check each of your potential solutions. \(\sqrt{5 n+1}-6=-4\)

Find the following products and express answers in simplest radical form. All variables represent nonnegative real numbers. \(\sqrt{3}(\sqrt{7}+\sqrt{10})\)

Use the distributive property to help simplify each of the following. \(\frac{-2 \sqrt{20}}{3}+\frac{3 \sqrt{45}}{4}-\frac{5 \sqrt{80}}{6}\)

Evaluate each of the following. For example, \(\sqrt{25}=5\). \(\sqrt{\frac{144}{36}}\)

Simplify each numerical expression. \(3^{-4} \cdot 3^{6}\)

Write each of the following in scientific notation. For example \(27800=(2.78)(10)^{4}\). \(0.00000000194\)

Evaluate each numerical expression. \((-1)^{\frac{7}{3}}\)

Solve each equation. Don't forget to check each of your potential solutions. \(\sqrt{2 x-5}=-1\)

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

Use the distributive property to help simplify each of the following. \(5 \sqrt[3]{3}+2 \sqrt[3]{24}-6 \sqrt[3]{81}\)

Evaluate each of the following. For example, \(\sqrt{25}=5\). \(\sqrt[3]{\frac{27}{64}}\)

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

Write each of the following in scientific notation. For example \(27800=(2.78)(10)^{4}\). \(0.00000000003\)

Evaluate each numerical expression. \((-8)^{\frac{4}{3}}\)

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

Find the following products and express answers in simplest radical form. All variables represent nonnegative real numbers. \(5 \sqrt{6}(2 \sqrt{5}-3 \sqrt{11})\)

Use the distributive property to help simplify each of the following. \(-3 \sqrt[3]{2}-2 \sqrt[3]{16}+\sqrt[3]{54}\)

Evaluate each of the following. For example, \(\sqrt{25}=5\). \(\sqrt[3]{-\frac{8}{27}}\)

Simplify each numerical expression. \(10^{4} \cdot 10^{-6}\)

For Problems \(19-32\), write each of the following in ordinary decimal notation. For example, \((3.18)(10)^{2}=318\). \((2.3)(10)^{1}\)

Solve each equation. Don't forget to check each of your potential solutions. \(\sqrt{5 x+2}=\sqrt{6 x+1}\)

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

Evaluate each of the following. For example, \(\sqrt{25}=5\). \(\sqrt[3]{8^{3}}\)

Simplify each numerical expression. \(10^{-1} \cdot 10^{-2}\)

For Problems \(19-32\), write each of the following in ordinary decimal notation. For example, \((3.18)(10)^{2}=318\). \((1.62)(10)^{2}\)

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

Find the following products and express answers in simplest radical form. All variables represent nonnegative real numbers. \(4 \sqrt{2}(3 \sqrt{12}+7 \sqrt{6})\)

Use the distributive property to help simplify each of the following. \(4 \sqrt[3]{24}-6 \sqrt[3]{3}+13 \sqrt[3]{81}\)

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

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

For Problems \(19-32\), write each of the following in ordinary decimal notation. For example, \((3.18)(10)^{2}=318\). \((4.19)(10)^{3}\)

Evaluate each numerical expression. \(\left(\frac{27}{8}\right)^{\frac{4}{3}}\)

Solve each equation. Don't forget to check each of your potential solutions. \(\sqrt{3 x+1}=\sqrt{7 x-5}\)

Find the following products and express answers in simplest radical form. All variables represent nonnegative real numbers. \(-4 \sqrt{5}(2 \sqrt{5}+4 \sqrt{12})\)

Express each of the following in simplest radical form. All variables represent positive real numbers. \(\sqrt{32 x}\)

For Problems \(21-74\), change each radical to simplest radical form. \(\sqrt{27}\)

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

For Problems \(19-32\), write each of the following in ordinary decimal notation. For example, \((3.18)(10)^{2}=318\). \((7.631)(10)^{4}\)

Evaluate each numerical expression. \(\left(\frac{8}{125}\right)^{\frac{2}{3}}\)

Solve each equation. Don't forget to check each of your potential solutions. \(\sqrt{6 x+5}=\sqrt{2 x+10}\)

Find the following products and express answers in simplest radical form. All variables represent nonnegative real numbers. \(-5 \sqrt{3}(3 \sqrt{12}-9 \sqrt{8})\)

Express each of the following in simplest radical form. All variables represent positive real numbers. \(\sqrt{50 y}\)

Change each radical to simplest radical form. \(\sqrt{48}\)

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

For Problems \(19-32\), write each of the following in ordinary decimal notation. For example, \((3.18)(10)^{2}=318\). \((5)(10)^{8}\)