Simplifying Radicals and Radical Operations

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

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

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The product of two radicals can be simplified by multiplying the numbers under the radicals together, then simplifying the resulting radical.

$$\text{√}\frac{a}{b}$$ .

$$16\text{√}6$$ .

You can only add radicals that have the same index and radicand. For example, $$3\text{√}2 + 2\text{√}2 = 5\text{√}2$$ .

$$2\text{√}5$$ .

$$\text{√}7$$ .

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