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, factor the number under the radical into its prime factors and look for pairs (for square roots) or triplets (for cube roots) to simplify.

The square root of 16 is 4, since 4 x 4 = 16.

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

The sum is $$3\text{√}2$$ after simplifying.

To divide radical expressions, divide the numbers under the radicals and simplify. For example, $$\frac{\text{√}15}{\text{√}10} = \text{√}\frac{15}{10} = \text{√}\frac{3}{2}$$ .

The result is $$6\text{√}2 - 6$$ after distributing.

The formula is (a + b)(c + d) = ac + ad + bc + bd. Apply this to radicals as well.

The simplified form is $$35 + 7\text{√}3 - 5\text{√}2 - \text{√}6$$ .

Rationalizing the denominator means to eliminate any radicals in the denominator of a fraction.