91Ó°ÊÓ

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

In \(11-38,\) evaluate each expression in the set of real numbers. $$ \sqrt[3]{\frac{8}{27}} $$

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

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

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

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

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

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