Chapter 5

For Problems \(1-20\), 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. \(2^{7} \cdot 2^{-3}\)

For Problems \(1-18\), write each of the following in scientific notation. \(0.00000082\)

For Problems \(1-30\), evaluate each numerical expression. $$ 4^{\frac{7}{2}} $$

For Problems 1-56, 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. $$ \sqrt{3}(\sqrt{7}+\sqrt{10}) $$

For Problems \(1-20\), 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. \(3^{-4} \cdot 3^{6}\)

For Problems \(1-18\), write each of the following in scientific notation. \(0.00000000194\)

For Problems 1-56, 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. $$ 3 \sqrt{5}(2 \sqrt{2}-\sqrt{7}) $$

For Problems \(1-20\), 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. \(10^{-5} \cdot 10^{2}\)

For Problems \(1-18\), write each of the following in scientific notation. \(0.00000000003\)

For Problems \(1-30\), evaluate each numerical expression. $$ (-8)^{\frac{4}{3}} $$

For Problems 1-56, 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. $$ 5 \sqrt{6}(2 \sqrt{5}-3 \sqrt{11}) $$

For Problems \(1-20\), 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. (Objective 2 ) For example, $$ (3.18)\left(10^{2}\right)=318 $$ $$ (2.3)\left(10^{1}\right) $$

For Problems \(1-30\), evaluate each numerical expression. $$ -4^{\frac{5}{2}} $$

For Problems 1-56, 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. $$ (1.62)\left(10^{2}\right) $$

For Problems \(1-30\), evaluate each numerical expression. $$ -16^{\frac{3}{2}} $$

For Problems 1-56, 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. $$ 4 \sqrt{2}(3 \sqrt{12}+7 \sqrt{6}) $$

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. $$ (4.19)\left(10^{3}\right) $$

For Problems \(1-30\), evaluate each numerical expression. $$ \left(\frac{27}{8}\right)^{\frac{4}{3}} $$

For Problems 1-56, 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. $$ -4 \sqrt{5}(2 \sqrt{5}+4 \sqrt{12}) $$

For Problems \(21-64\), express each of the following in simplest radical form. All variables represent positive real numbers. $$ \sqrt{32 x} $$

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. $$ (7.631)\left(10^{4}\right) $$

For Problems \(1-30\), evaluate each numerical expression. $$ \left(\frac{8}{125}\right)^{\frac{2}{3}} $$

For Problems 1-56, 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. $$ -5 \sqrt{3}(3 \sqrt{12}-9 \sqrt{8}) $$

For Problems \(21-64\), 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. $$ (5)\left(10^{8}\right) $$