Multiplying Radicals

A radical is an expression that includes a root, such as a square root (√) or cube root (∛). It represents the operation of finding a number that, when multiplied by itself a certain number of times, gives the original number.

The product of two radicals can be simplified by multiplying the numbers inside the radicals together. For example, $$\text{If } a = \text{√}x \text{ and } b = \text{√}y, \text{ then } a \times b = \text{√}(xy)$$ .

$$60\text{√}7$$ .

The square root of a product is equal to the product of the square roots. For example, $$\text{√}(ab) = \text{√}a \times \text{√}b$$ .

$$12\text{√}2$$ .

$$\text{√}(-1) = i$$ , where i is the imaginary unit.

Like radicals are radicals that have the same index and the same radicand. For example, $$\text{√}2 \text{ and } 3\text{√}2$$ are like radicals.

To simplify a radical expression, factor the radicand into its prime factors, then pair the factors to take them out of the radical.

$$6\text{√}2$$ .

$$\text{√}(ab)$$ .