91Ó°ÊÓ

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 \(3-38\) 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. $$ \sqrt[4]{48}-\sqrt[4]{3} $$

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.

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

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

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

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

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