Simplifying Radical Expressions

Product Property of Radicals For any numbers a and b where and ,

Product Property of Radicals Examples

Quotient Property of Radicals For any numbers a and b where and ,

Examples:

Examples:

Rationalizing the denominator Rationalizing the denominator means to remove any radicals from the denominator. Ex: Simplify

Simplest Radical Form No perfect nth power factors other than 1. No fractions in the radicand. No radicals in the denominator.

Examples:

Examples:

Reverse of the Distributive Property Adding radicals We can only combine terms with radicals if we have like radicals Reverse of the Distributive Property

Examples:

Examples:

Multiplying radicals - Distributive Property

Multiplying radicals - FOIL

Examples:

Examples:

where a, b, c, d are rational numbers. Conjugates Binomials of the form where a, b, c, d are rational numbers.

The product of conjugates is a rational number The product of conjugates is a rational number. Therefore, we can rationalize denominator of a fraction by multiplying by its conjugate.

Examples:

Examples: