1. Radical Review Simplify radical expressions. Rationalize fractions with radicals in the denominator.

2. How to Simplify Radical Expressions  A radicand is an expression contained within the radical symbol (√ ).  An expression that contains the radical symbol is simplified just when: 1.No radicand has a perfect square factor other than 1. 2.No radicand contains a fraction. 3.No radical appears in the denominator.

3. The Product and Quotient Rules In the simplification of radical expressions, we will use two rules: The Product Rule: the square root of a product is the product of square roots. In symbols: The Quotient Rule: the square root of a quotient is the quotient of the square roots. In symbols:

4. Example: The Product Rule Make use of the product rule to simply the radical expression: Strategy: find all perfect square factors of 108, write 108 as the product of those factors and whatever else remains, and then use the Product Rule to simplify.

5. Example: The Quotient Rule When we simplify a radical expression, we cannot leave a fraction under the radical. To simplify when a fraction is under the radical, use the Quotient Rule. Simplify

8. Rationalization We cannot allow a fraction to remain under a radical. Nor can we allow a radical expression to remain in a denominator. Rationalization is the process wherein we remove a radical expression from the denominator of a fraction. To remove a monomial radical expression from a denominator, simply multiply by it on both top and bottom of the fraction. To remove a binomial radical expression from a denominator, multiply both top and bottom by its conjugate. The conjugate of the binomial a + b is a - b; and the conjugate of the binomial a - b is a + b.

9. Simplify