Operations with Radicals word problems

A radical is a symbol that represents the root of a number, most commonly the square root. For example, $$\sqrt{4}$$ equals 2.

To simplify a radical expression, factor the number under the radical into its prime factors and look for pairs of factors. For example, $$\sqrt{18} = \sqrt{9 \cdot 2} = 3\sqrt{2}$$ .

The perimeter of a rectangle is calculated by the formula: P = 2(length + width).

The area of a rectangle is found using the formula: A = length × width.

The perimeter is the total distance around the rectangle, which depends on the lengths of all four sides.

The area is given by the expression: A = $$a \cdot b$$ .

Expressing an answer in simplified radical form means to reduce the radical to its simplest form, removing any perfect squares from under the radical.

To add or subtract radical expressions, combine like terms. For example, $$\sqrt{2} + 3\sqrt{2} = 4\sqrt{2}$$ .

The perimeter is $$16\sqrt{2} cm$$ .

Subtract the sum of the known sides from the total perimeter to find the length of the remaining side.