Simplifying Radicals

A radical is a symbol that represents the root of a number, most commonly the square root. For example, $$\text{√}x$$ represents the square root of x.

To simplify a radical, factor the number under the radical into its prime factors and look for pairs of factors. Each pair can be taken out of the radical as a single factor.

$$2\text{√}6$$

$$5x^2\text{√}2$$

$$5\text{√}3$$

$$2\text{√}7$$

$$3\text{√}5$$

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

The product property states that $$\text{√}(a \times b) = \text{√}a \times \text{√}b$$ for any non-negative numbers a and b.

The quotient property states that $$\text{√}(a/b) = \text{√}a / \text{√}b$$ for any non-negative numbers a and b, where b ≠ 0.