Chapter 5

For Problems \(1-18\), write each of the following in scientific notation. For example, $$ 27,800=(2.78)\left(10^{4}\right) $$ 89

For Problems \(1-30\), evaluate each numerical expression. $$ 81^{\frac{1}{2}} $$

For Problems 1-56, solve each equation. Don't forget to check each of your potential solutions. $$ \sqrt{5 x}=10 $$

For Problems \(1-14\), multiply and simplify where possible. $$ \sqrt{6} \sqrt{12} $$

For Problems \(1-20\), use the distributive property to help simplify each of the following. For example, $$ \begin{aligned} 3 \sqrt{8}-\sqrt{32} &=3 \sqrt{4} \sqrt{2}-\sqrt{16} \sqrt{2} \\ &=3(2) \sqrt{2}-4 \sqrt{2} \\ &=6 \sqrt{2}-4 \sqrt{2} \\ &=(6-4) \sqrt{2}=2 \sqrt{2} \end{aligned} $$ $$ 5 \sqrt{18}-2 \sqrt{2} $$

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

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

For Problems \(1-18\), write each of the following in scientific notation. 117

For Problems \(1-30\), evaluate each numerical expression. $$ 64^{\frac{1}{2}} $$

For Problems 1-56, solve each equation. Don't forget to check each of your potential solutions. $$ \sqrt{3 x}=9 $$

For Problems \(1-14\), multiply and simplify where possible. $$ \sqrt{8} \sqrt{6} $$

For Problems \(1-20\), use the distributive property to help simplify each of the following. For example, $$ \begin{aligned} 3 \sqrt{8}-\sqrt{32} &=3 \sqrt{4} \sqrt{2}-\sqrt{16} \sqrt{2} \\ &=3(2) \sqrt{2}-4 \sqrt{2} \\ &=6 \sqrt{2}-4 \sqrt{2} \\ &=(6-4) \sqrt{2}=2 \sqrt{2} \end{aligned} $$ $$ 7 \sqrt{12}+4 \sqrt{3} $$

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

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

For Problems \(1-18\), write each of the following in scientific notation. 4290

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

For Problems 1-56, solve each equation. Don't forget to check each of your potential solutions. $$ \sqrt{2 x}+4=0 $$

For Problems \(1-14\), multiply and simplify where possible. $$ (3 \sqrt{3})(2 \sqrt{6}) $$

For Problems \(1-20\), use the distributive property to help simplify each of the following. For example, $$ \begin{aligned} 3 \sqrt{8}-\sqrt{32} &=3 \sqrt{4} \sqrt{2}-\sqrt{16} \sqrt{2} \\ &=3(2) \sqrt{2}-4 \sqrt{2} \\ &=6 \sqrt{2}-4 \sqrt{2} \\ &=(6-4) \sqrt{2}=2 \sqrt{2} \end{aligned} $$ $$ 7 \sqrt{12}+10 \sqrt{48} $$

Evaluate each of the following. For example, \(\sqrt{25}=5\). \(-\sqrt{100}\)

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

For Problems \(1-18\), write each of the following in scientific notation. 812,000

For Problems \(1-30\), evaluate each numerical expression. $$ (-32)^{\frac{1}{5}} $$

For Problems 1-56, solve each equation. Don't forget to check each of your potential solutions. $$ \sqrt{4 x}+5=0 $$

For Problems \(1-14\), multiply and simplify where possible. $$ (5 \sqrt{2})(3 \sqrt{12}) $$

For Problems \(1-20\), use the distributive property to help simplify each of the following. For example, $$ \begin{aligned} 3 \sqrt{8}-\sqrt{32} &=3 \sqrt{4} \sqrt{2}-\sqrt{16} \sqrt{2} \\ &=3(2) \sqrt{2}-4 \sqrt{2} \\ &=6 \sqrt{2}-4 \sqrt{2} \\ &=(6-4) \sqrt{2}=2 \sqrt{2} \end{aligned} $$ $$ 6 \sqrt{8}-5 \sqrt{18} $$

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

Simplify each numerical expression. \(10^{-3}\)

For Problems \(1-18\), write each of the following in scientific notation. \(6,120,000\)

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

For Problems 1-56, solve each equation. Don't forget to check each of your potential solutions. $$ 2 \sqrt{n}=5 $$

For Problems \(1-14\), multiply and simplify where possible. $$ (4 \sqrt{2})(-6 \sqrt{5}) $$

For Problems \(1-20\), use the distributive property to help simplify each of the following. For example, $$ \begin{aligned} 3 \sqrt{8}-\sqrt{32} &=3 \sqrt{4} \sqrt{2}-\sqrt{16} \sqrt{2} \\ &=3(2) \sqrt{2}-4 \sqrt{2} \\ &=6 \sqrt{2}-4 \sqrt{2} \\ &=(6-4) \sqrt{2}=2 \sqrt{2} \end{aligned} $$ $$ -2 \sqrt{50}-5 \sqrt{32} $$

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

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

For Problems \(1-18\), write each of the following in scientific notation. \(72,400,000\)

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

For Problems 1-56, solve each equation. Don't forget to check each of your potential solutions. $$ 5 \sqrt{n}=3 $$

For Problems \(1-14\), multiply and simplify where possible. $$ (-7 \sqrt{3})(2 \sqrt{5}) $$

For Problems \(1-20\), use the distributive property to help simplify each of the following. For example, $$ \begin{aligned} 3 \sqrt{8}-\sqrt{32} &=3 \sqrt{4} \sqrt{2}-\sqrt{16} \sqrt{2} \\ &=3(2) \sqrt{2}-4 \sqrt{2} \\ &=6 \sqrt{2}-4 \sqrt{2} \\ &=(6-4) \sqrt{2}=2 \sqrt{2} \end{aligned} $$ $$ -2 \sqrt{20}-7 \sqrt{45} $$

Evaluate each of the following. For example, \(\sqrt{25}=5\). \(\sqrt[3]{216}\)

Simplify each numerical expression. \(\frac{1}{2^{-6}}\)

For Problems \(1-18\), write each of the following in scientific notation. \(40,000,000\)

For Problems 1-56, solve each equation. Don't forget to check each of your potential solutions. $$ 3 \sqrt{n}-2=0 $$

For Problems \(1-14\), multiply and simplify where possible. $$ (-3 \sqrt{3})(-4 \sqrt{8}) $$

For Problems \(1-20\), use the distributive property to help simplify each of the following. For example, $$ \begin{aligned} 3 \sqrt{8}-\sqrt{32} &=3 \sqrt{4} \sqrt{2}-\sqrt{16} \sqrt{2} \\ &=3(2) \sqrt{2}-4 \sqrt{2} \\ &=6 \sqrt{2}-4 \sqrt{2} \\ &=(6-4) \sqrt{2}=2 \sqrt{2} \end{aligned} $$ $$ 3 \sqrt{20}-\sqrt{5}-2 \sqrt{45} $$

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

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

For Problems \(1-18\), write each of the following in scientific notation. \(500,000,000\)

For Problems 1-56, solve each equation. Don't forget to check each of your potential solutions. $$ 2 \sqrt{n}-7=0 $$