Multiplying and Dividing Radicals

A radical is an expression that includes a root, such as a square root (√) or cube root (∛).

To multiply two radicals, multiply the numbers outside the radicals and the numbers inside the radicals separately. For example, $$\text{If } a = \text{√}m \text{ and } b = \text{√}n, \text{ then } a \times b = \text{√}(m \times n)$$ .

$$60\text{√}7$$ .

To divide radicals, divide the numbers outside the radicals and the numbers inside the radicals separately. For example, $$\frac{\text{√}m}{\text{√}n} = \text{√}\frac{m}{n}$$ .

$$10$$ .

$$\frac{2\text{√}2}{3}$$ .

$$4$$ .

$$\text{√}(a \times b)$$ .

$$m$$ .

Rationalizing the denominator involves eliminating any radicals in the denominator of a fraction.