Properties of Radicals 9.1 Properties of Radicals Students will be able to use properties of radicals to simplify expressions. Students will be able to simplify expressions by rationalizing the denominator. A radical expression is an expression that contains a radical.

An expression involving a radical with index n is in simplest form when these three conditions are met. No radicands have perfect nth powers as factors other than 1. No radicands contain fractions. No radicands appear in the denominator of a fraction. We will use the following properties of radicals to simplify radical expressions

Product Property of Radicals

Product Property of Radicals More examples

Product Property of Radicals You try

Quotient Property of Radicals

Quotient Property of Radicals More examples

Quotient Property of Radicals More examples

Quotient Property of Radicals You try

Rationalizing the Denominator When a radical is in the denominator of a fraction, you can multiply the fraction by an appropriate form of 1 to eliminate the radical from the denominator. This process is called rationalizing the donominator.

Rationalizing the Denominator You try