Warm Up: 1)2)

5.2 Notes: Properties of Rational Exponents and Radicals

Exponent Properties and Rational Exponents: All rational exponents follow the same rules as regular exponents, we just have to make sure we follow fraction rules as well!

Properties of Radicals Product property: Quotient property: Remember…these work both ways!

HW: P. 248 #3 – 20 ALL

Warm Up: Factor: 1) 3x 2 – 13x + 122) 16x 2 – 1213) x 3 – 125 Simplify: 4) 5) 6) Evaluate: 7) (x – 3) = 64208) - 21 = 7

Writing Radicals in Simplest Form Remember when we had, which isn’t a perfect square, so we had to simplify the radical? Well, we can do this for other roots as well.

Simplifying using conjugates…. Remember conjugates? We write the same term, but with a different sign in the middle. This is what we use to rationalize the radical denominator. ◦

Adding & Subtracting Like Radicals & Roots In order to add or subtract radicals, they have to be the same root with the same value under the radical. When we do add or subtract them, we are only working with the coefficients (values in front) of the radicals. The “stuff” under the radicals DO NOT CHANGE.

DUE IN CLASS: p. 248 #21 – 47 odd

Warm up:

Simplifying Variable Expressions:

Writing Expressions in Simplest Form:

Adding & Subtracting Variable Expressions These follow the same rules as regular radicals, just that not only do the numbers have to match under the radical but also the variables and their exponents. **You may have to reduce the radical to make the radicals match before performing the operation.

HW: p. 248 – 249 #49 – 69 odd