Objectives The student will be able to: 1. simplify square roots, and 2. rational the denominator

What numbers are perfect squares? 1 • 1 = 1 2 • 2 = 4 3 • 3 = 9 4 • 4 = 16 5 • 5 = 25 6 • 6 = 36 49, 64, 81, 100, 121, 144, ...

Simplify . Factors or 72 1 * 72 2 * 36 3 * 24 4 * 18 6 * 12 Chose the pair with the largest perfect square -  

Find a perfect square that goes into 147. Simplify Find a perfect square that goes into 147.

Find a perfect square that goes into 605. Simplify Find a perfect square that goes into 605.

How do you know when a radical problem is done? No radicals can be simplified. Example: There are no fractions in the radical. Example: There are no radicals in the denominator. Example:

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

There is a radical in the denominator! If the denominator is a factor of the numerator then the fraction simplifies Simplify. Divide the radicals. Uh oh… There is a radical in the denominator! Whew! It simplified!

If the denominator can be simplified and/or cancels with a numerator factor then the fraction simplifies Simplify   Uh oh… Another radical in the denominator! OR   Whew! It simplified again!   2

Rationalizing the denominator Rationalizing the denominator means to remove any radicals from the denominator. DO that by creating a perfect square in the denominator.  multiply by a fraction = 1 Ex: Simplify

Simplify Since the fraction doesn’t reduce, split the radical up. Uh oh… There is a fraction in the radical! Simplify Since the fraction doesn’t reduce, split the radical up. How do I get rid of the radical in the denominator? Multiply by the “fancy one” to make the denominator a perfect square!

This cannot be divided which leaves the radical in the denominator. Do not leave radicals in the denominator. So rationalize by multiplying the fraction by something to eliminate the radical in the denominator. 42 cannot be simplified, so we are finished.

Reduce the fraction.

Examples:

Examples:

Examples:

Examples: