SIMPLIFYING RADICALS Square Roots and Cube Roots Dr

SIMPLIFYING RADICALS Square Roots and Cube Roots Dr. Shildneck

SIMPLIFYING RADICAL EXPRESSIONS Goal: To “pull out” perfect square factors from under the radical.

SIMPLIFYING RADICAL EXPRESSIONS Important Property: But more importantly for us… We can take radicals and break them apart!

SIMPLIFYING SQUARE ROOTS Method One: Searching for Perfect Squares Ex 1 Simplify.

SIMPLIFYING SQUARE ROOTS Method One: Searching for Perfect Squares Ex 2 Simplify.

SIMPLIFYING SQUARE ROOTS So what happens if the numbers are more difficult and you have a hard time finding perfect squares? Method 2 – Prime Factorization 1. Break down the number using a factor tree 2. Find Pairs (perfect squares) to pull out (take the square root of). 3. Pull out a number for each pair and multiply the factors outside of the radical, and the numbers under the radical to simplify the expression.

SIMPLIFYING SQUARE ROOTS Method Two: Prime Factorization Ex 3 Simplify.

SIMPLIFYING SQUARE ROOTS Method Two: Prime Factorization Ex 4 Simplify.

SIMPLIFYING CUBE ROOTS For Cube Roots: Follow the same processes as you do for square roots, except you will look for perfect cubes (triples). Ex 5 Simplify.

SIMPLIFYING CUBE ROOTS Ex 6 Simplify.

SIMPLIFYING CUBE ROOTS Ex 7 Simplify.

SIMPLIFYING CUBE ROOTS Note. A negative times itself 3 times is negative!