Operations with Radicals

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

To simplify a radical expression means to rewrite it in a simpler form, often by removing perfect squares or cubes from under the radical sign.

The product property states that $$\text{√}(a) \times \text{√}(b) = \text{√}(a \times b)$$ .

The quotient property states that $$\text{√}(a/b) = \text{√}(a) / \text{√}(b)$$ , provided that b is not zero.

To multiply two radicals, use the product property: $$\text{√}(a) \times \text{√}(b) = \text{√}(a \times b)$$ .

The value of $$\text{√}(4)$$ is 2.

$$\text{√}(18) = \text{√}(9 \times 2) = 3\text{√}(2)$$ .

The result is $$-24\text{√}(6)$$ .

The result is $$3\text{√}(5)$$ .

$$\text{√}(\frac{4}{64}) = \frac{2}{8} = \frac{1}{4}$$ .