Chapter 3

The dimensions of a rectangular solid are \(\sqrt{5}\) inches by \((2+\sqrt{3})\) inches by \((2-\sqrt{3})\) inches. Express the volume of the solid in simplest form.

In \(43-46,\) solve each equation for the variable. $$ a^{2}=196 $$

In \(43-47,\) express each answer in simplest radical form. The length of each of the two congruent sides of an isosceles triangle is \(\sqrt{500}\) feet and the length of the third side is \(\sqrt{45}\) feet. What is the perimeter of the triangle?

Solve and check each equation. \(5 x-\sqrt{12}=\sqrt{108}-3 x\)

The area of a circular pool is 5\(x^{2} y^{4} \pi\) square meters. Express the radius of the pool in sim- plest radical form.

The lengths of the legs of a right triangle in feet are \((3+\sqrt{3})\) and \((3-\sqrt{3})\) a. Find the length of the hypotenuse of the triangle. b. Express, in simplest form, the perimeter of the triangle. c. What is the area of the triangle?

In \(43-46,\) solve each equation for the variable. $$ b^{2}=100 $$

In \(43-47,\) express each answer in simplest radical form. The lengths of the legs of a right triangle are \(\sqrt{18}\) centimeters and \(\sqrt{32}\) centimeters. a. Find the length of the hypotenuse. b. Find the perimeter of the triangle.

Solve and check each equation. \(y \sqrt{3}+1=3-y\)

The radius of the surface of a circular pool is \(\left(2+\sqrt{x y^{5}}\right)\) meters. Express the area of the pool in simplest form.

In \(43-46,\) solve each equation for the variable. $$ y^{2}-169=0 $$

In \(43-47,\) express each answer in simplest radical form. The length of each leg of an isosceles right triangle is \(\sqrt{98}\) inches. a. Find the length of the hypotenuse. b. What is the perimeter of the triangle?

Solve and check each equation. \(7-b \sqrt{8}=b \sqrt{5}+4\)

The area of a square is 14 square centimeters. What is the length of a side of the square?

In \(43-47,\) express each answer in simplest radical form. The dimensions of a rectangle are \(\sqrt{250}\) meters and \(\sqrt{1,440}\) meters. a. Express the perimeter of the rectangle in simplest radical form. b. Express the length of the diagonal of the rectangle in simplest radical form.

The area of a rectangle is 24 square inches. The length of the rectangle is \(\sqrt{5}+1\) inches. Express the width of the rectangle in simplest form.

Find the length of the hypotenuse of a right triangle if the length of the longer leg is 20 feet and the length of the shorter leg is 12 feet.

The perimeter of an isosceles triangle is \(\sqrt{50}\) feet. The lengths of the sides are in the ratio \(3 : 3 : 4\) . Find the length of each side of the triangle.

Find the length of the shorter leg of a right triangle if the length of the longer leg is 36 inches and the length of the hypotenuse is 39 inches.

What is the length of a side of a square if the length of a diagonal is \(\sqrt{72}\) inches?