Radical Operations

A radical is a symbol that represents the root of a number, most commonly the square root. For example, $$\text{the square root of } 9 \text{ is represented as } \sqrt{9} = 3$$ .

The square root of a perfect square is an integer or whole number. For example, $$\text{the square root of } 16 \text{ is } 4$$ .

$$\frac{\text{sqrt}(90)}{3} = \frac{3\text{sqrt}(10)}{3} = \text{sqrt}(10)$$ .

The product of two square roots can be simplified as follows: $$\text{If } a \text{ and } b \text{ are non-negative, then } \sqrt{a} \times \sqrt{b} = \sqrt{a \times b}$$ .

$$\text{sqrt}(6)(\text{sqrt}(6) + \text{sqrt}(10)) = 6 + 2\text{sqrt}(15)$$ .

The sum of two square roots cannot always be simplified. For example, $$\text{sqrt}(2) + \text{sqrt}(3)$$ cannot be simplified further.

$$4\text{sqrt}(5)(3 + \text{sqrt}(10)) = 12\text{sqrt}(5) + 4\text{sqrt}(50) = 12\text{sqrt}(5) + 20\text{sqrt}(2)$$ .

A perfect square is an integer that is the square of an integer. For example, 1, 4, 9, and 16 are perfect squares.

$$\text{sqrt}(90) = 3\text{sqrt}(10)$$ .

The square root of 0 is 0, as $$\text{sqrt}(0) = 0$$ .