8.2.1 Radical Expressions and Rational Exponents (continued) Example 2 Simplifying Radical Expressions Properties of n th Roots (for a > 0 and b > 0) Product Property of Roots: The n th root of a product is equal to the product of the n th roots ab a b n n n = ⋅ Quotient Property of Roots: The n th root of a quotient is equal to the quotient of the n th roots.
n n
a b
a b
n
=
These properties of n th roots can be used to simplify radical expressions. When simplifying radical expressions, keep in mind that • the radical sign indicates only the principal or positive root for a number that has more than one real root, and • a denominator containing a radical must be rationalized.
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