Chapter 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. $$ \frac{\sqrt[4]{c^{6}}}{\sqrt[5]{c^{3}}} $$

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. $$ \sqrt{\frac{15}{8 b^{3}}} $$

The temperature on Mars roughly satisfies the inequality \(|t-75| \leq 145\) where \(t\) is the temperature in Fahrenheit. What is the range of temperatures on Mars?

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

In \(3-38,\) solve each equation for the variable, check, and write the solution set. $$ 3+\sqrt{4 x-3}=2 x $$

In \(11-38,\) evaluate each expression in the set of real numbers. $$ \sqrt[5]{-\frac{1}{32}} $$

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. $$ \sqrt[3]{2}+\sqrt[3]{16} $$

Rationalize the denominator and write each fraction in simplest form. All variables represent positive numbers. \(\frac{6-\sqrt{7}}{4-\sqrt{7}}\)

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. $$ \frac{\sqrt[3]{24 w^{2}}}{\sqrt[3]{3 w^{4}}} $$

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. $$ \sqrt{\frac{4 a^{3}}{27 b^{3}}} $$

Elevation of land in the United States is given by the inequality \(|h-10,019| \leq 10,301\) where \(h\) is the height in feet. What is the range of elevations in the United States?

In \(3-41\) , express each product in simplest form. Variables in the radicand with an even index are non-negative. $$ \sqrt{12 x y^{3}}(\sqrt{3 x y}+3) $$

In \(11-38,\) evaluate each expression in the set of real numbers. $$ \sqrt[3]{0.001} $$

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. $$ \sqrt[3]{54}+\sqrt[3]{128} $$

Rationalize the denominator and write each fraction in simplest form. All variables represent positive numbers. \(\frac{\sqrt{10}-1}{\sqrt{10}+1}\)

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. $$ \frac{\sqrt{64 x^{4}}+\sqrt[4]{40 x^{6}}}{\sqrt[4]{x^{6}}} $$

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. $$ \sqrt{\frac{9}{50 x y^{7}}} $$

In \(3-41\) , express each product in simplest form. Variables in the radicand with an even index are non-negative. $$ (1+\sqrt{5})(3-\sqrt{5}) $$

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

In \(11-38,\) evaluate each expression in the set of real numbers. $$ \sqrt[4]{0.0256} $$

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. $$ \sqrt[4]{48}-\sqrt[4]{3} $$

Rationalize the denominator and write each fraction in simplest form. All variables represent positive numbers. \(\frac{7+\sqrt{5}}{7-\sqrt{5}}\)

The area of a rectangle is 25\(\sqrt{35}\) square feet and the width is 10\(\sqrt{5}\) feet. Find the length of the rectangle in simplest radical form.

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. $$ \sqrt{\frac{8 x}{5 y^{3}}} $$

In \(3-41\) , express each product in simplest form. Variables in the radicand with an even index are non-negative. $$ (9+\sqrt{2 b})(1+\sqrt{2 b}) $$

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

In \(11-38,\) evaluate each expression in the set of real numbers. $$ \sqrt{x^{6}}, x \geq 0 $$

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. $$ \sqrt{9 x}+\sqrt{25 x} $$

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

The area of a right triangle is 6\(\sqrt{2}\) square centimeters and the length of one leg is \(\sqrt{12}\) cenimeters. What is the length of the other leg? What is the length of the hypotenuse?

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. $$ \sqrt{0.5} $$

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

In \(3-38,\) solve each equation for the variable, check, and write the solution set. $$ 2+\sqrt[3]{3 b-2}=6 $$

In \(11-38,\) evaluate each expression in the set of real numbers. $$ \sqrt{100 c^{4}}, c \geq 0 $$

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. $$ \sqrt{100 y}-\sqrt{25 y} $$

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

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. $$ \sqrt{2.42 a b^{5}} $$

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

In \(11-38,\) evaluate each expression in the set of real numbers. $$ \sqrt{0.25 x^{2}}, x \geq 0 $$

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. $$ \sqrt{8 a}-\sqrt{2 a} $$

Rationalize the denominator and write each fraction in simplest form. All variables represent positive numbers. \(\frac{4}{\sqrt{z}+8}\)

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. $$ \sqrt{0.001 x^{3}} $$

In \(3-41\) , express each product in simplest form. Variables in the radicand with an even index are non-negative. $$ (x-\sqrt[4]{3 y})(2 x-\sqrt[4]{3 y}) $$

In \(3-38,\) solve each equation for the variable, check, and write the solution set. $$ -10+\sqrt[4]{n-2}=-8 $$

In \(11-38,\) evaluate each expression in the set of real numbers. $$ \sqrt[3]{\frac{1,000}{a^{3}},} a \neq 0 $$

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. $$ \sqrt{18 b^{2}}+\sqrt{800 b^{2}} $$

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

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. $$ \sqrt{128 x^{2}} $$

In \(3-41\) , express each product in simplest form. Variables in the radicand with an even index are non-negative. $$ (\sqrt{6}+6)(\sqrt{6}-7) $$

In \(3-38,\) solve each equation for the variable, check, and write the solution set. $$ \sqrt{x+5}=1+\sqrt{x} $$