Simplifying Radicals

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

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

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$$2\text{√}3$$ because $$12 = 4 \times 3 = 2^2 \times 3$$ .

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

The quotient property states that $$\text{√}(a/b) = \text{√}a / \text{√}b$$ , provided that @@b eq 0@@.

$$15\text{√}5$$ because $$125 = 25 \times 5 = 5^2 \times 5$$ .

$$2\text{√}7$$ because $$28 = 4 \times 7 = 2^2 \times 7$$ .

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

$$5\text{√}2$$ because $$50 = 25 \times 2 = 5^2 \times 2$$ .