Chapter 3

In \(3-41\) , express each product in simplest form. Variables in the radicand with an even index are non-negative. $$ (-2 \sqrt{5})^{2} $$

In \(11-38,\) evaluate each expression in the set of real numbers. $$ \sqrt{625} $$

In \(3-38\) write each expression in simplest form. Variables in the radicand with an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero. $$ x \sqrt{32 x}+\sqrt{128 x^{3}} $$

Rationalize the denominator and write each fraction in simplest form. All variables represent positive numbers. \(\frac{\sqrt{24}}{2 \sqrt{6}}\)

In \(3-29\) write each quotient in simplest form. Variables in the radicand with an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero. $$ \frac{3}{\sqrt{3} x} $$

In \(3-38\) , write each radical in simplest radical form. Variables in the radicand of an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero. $$ \sqrt[3]{24} $$

In \(3-14,\) determine whether each of the numbers is rational or irrational. $$ 2 \frac{1}{3}+\sqrt{3} $$

In \(3-41\) , express each product in simplest form. Variables in the radicand with an even index are non-negative. $$ \sqrt{x^{3}} \cdot \sqrt{4 x} $$

In \(11-38,\) evaluate each expression in the set of real numbers. $$ \sqrt{169} $$

In \(3-38\) write each expression in simplest form. Variables in the radicand with an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero. $$ 4 b \sqrt{24 b^{3}}+\sqrt{54 b^{5}} $$

Rationalize the denominator and write each fraction in simplest form. All variables represent positive numbers. \(\frac{1}{3+\sqrt{5}}\)

In \(3-29\) write each quotient in simplest form. Variables in the radicand with an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero. $$ \frac{7}{\sqrt{7 y}} $$

In \(3-38\) , write each radical in simplest radical form. Variables in the radicand of an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero. $$ \cdot \frac{1}{2} \sqrt{7} 2 a b^{5} $$

In \(3-41\) , express each product in simplest form. Variables in the radicand with an even index are non-negative. $$ 2 \sqrt{a b} \cdot 2 \sqrt{a b^{2}} $$

In \(3-38,\) solve each equation for the variable, check, and write the solution set. $$ 8+\sqrt{2 x-1}=15 $$

In \(11-38,\) evaluate each expression in the set of real numbers. $$ -\sqrt{0.04} $$

In \(3-38\) write each expression in simplest form. Variables in the radicand with an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero. $$ 3 x^{3} \sqrt{80}+2 \sqrt{125 x^{6}} $$

Rationalize the denominator and write each fraction in simplest form. All variables represent positive numbers. \(\frac{1}{5-\sqrt{2}}\)

In \(3-29\) write each quotient in simplest form. Variables in the radicand with an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero. $$ \frac{\sqrt{12 a^{2}}}{\sqrt{4 a}} $$

In \(3-38\) , write each radical in simplest radical form. Variables in the radicand of an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero. $$ \sqrt[3]{40 a^{4}} $$

In \(15-26,\) find and graph the solution set of each inequality. $$ |a-5| \geq 3 $$

In \(3-41\) , express each product in simplest form. Variables in the radicand with an even index are non-negative. $$ \sqrt{5 y} \cdot \sqrt{4 y^{3}} $$

In \(3-38,\) solve each equation for the variable, check, and write the solution set. $$ \sqrt{5 x+2}=\sqrt{9 x-14} $$

In \(11-38,\) evaluate each expression in the set of real numbers. $$ \pm \sqrt{0.64} $$

In \(3-38\) write each expression in simplest form. Variables in the radicand with an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero. $$ \sqrt{5}+\sqrt{\frac{1}{5}} $$

Rationalize the denominator and write each fraction in simplest form. All variables represent positive numbers. \(\frac{1}{1+\sqrt{3}}\)

In \(3-29\) write each quotient in simplest form. Variables in the radicand with an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero. $$ \frac{\sqrt{18 c^{3}}}{\sqrt{9 c}} $$

In \(3-38\) , write each radical in simplest radical form. Variables in the radicand of an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero. $$ \sqrt{\frac{3 x}{4 y}} $$

In \(15-26,\) find and graph the solution set of each inequality. $$ |2 y+5| > 9 $$

In \(3-41\) , express each product in simplest form. Variables in the radicand with an even index are non-negative. $$ \sqrt{x^{5} y^{3}} \cdot \sqrt{3 x y} $$

In \(3-38,\) solve each equation for the variable, check, and write the solution set. $$ \sqrt{20-2 x}=\sqrt{5 x-8} $$

In \(11-38,\) evaluate each expression in the set of real numbers. $$ \sqrt{1.44} $$

In \(3-38\) write each expression in simplest form. Variables in the radicand with an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero. $$ \sqrt{24}+2 \sqrt{\frac{3}{2}} $$

Rationalize the denominator and write each fraction in simplest form. All variables represent positive numbers. \(\frac{4}{3-\sqrt{3}}\)

In \(3-29\) write each quotient in simplest form. Variables in the radicand with an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero. $$ \frac{4 \sqrt{2}+8 \sqrt{12}}{2 \sqrt{2}} $$

In \(3-38\) , write each radical in simplest radical form. Variables in the radicand of an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero. $$ \sqrt{\frac{4 a^{4}}{25}} $$

In \(15-26,\) find and graph the solution set of each inequality. $$ |2-4 b| \leq 6 $$

In \(3-41\) , express each product in simplest form. Variables in the radicand with an even index are non-negative. $$ 7 \sqrt{a} \cdot 5 \sqrt{\frac{a}{9}} $$

In \(3-38,\) solve each equation for the variable, check, and write the solution set. $$ x=\sqrt{4 x+5} $$

In \(11-38,\) evaluate each expression in the set of real numbers. $$ \sqrt[3]{27} $$

In \(3-38\) write each expression in simplest form. Variables in the radicand with an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero. $$ 14 \sqrt{\frac{1}{7}}+\sqrt{28} $$

Rationalize the denominator and write each fraction in simplest form. All variables represent positive numbers. \(\frac{3}{1+\sqrt{5}}\)

In \(3-29\) write each quotient in simplest form. Variables in the radicand with an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero. $$ \frac{3 \sqrt{10}-9 \sqrt{50}}{3 \sqrt{5}} $$

In \(3-38\) , write each radical in simplest radical form. Variables in the radicand of an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero. $$ \sqrt{\frac{3 b^{3}}{44}} $$

In \(15-26,\) find and graph the solution set of each inequality. $$ |-5-a| > 4 $$

In \(3-41\) , express each product in simplest form. Variables in the radicand with an even index are non-negative. $$ \sqrt{\frac{x}{2}} \cdot \sqrt{\frac{x^{2}}{2}} $$

In \(11-38,\) evaluate each expression in the set of real numbers. $$ \sqrt[4]{16} $$

In \(3-38\) write each expression in simplest form. Variables in the radicand with an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero. $$ \sqrt{\frac{1}{2 x}}+\sqrt{\frac{1}{2 x}} $$

Rationalize the denominator and write each fraction in simplest form. All variables represent positive numbers. \(\frac{4}{4+\sqrt{7}}\)

In \(3-29\) write each quotient in simplest form. Variables in the radicand with an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero. $$ \frac{\sqrt{72}+\sqrt{54}}{\sqrt{18}} $$