1. Dividing Radicals
Note- Notes for rationalizing denominators are included in this powerpoint, yet students are not required to rationalize radical denominators on the SOL test. Students are expected to be able to divide radicals not required denominators to be rationalized.

2. Fractional Radicands

3. Fractional Radicands
Raise BOTH the numerator and the denominator to the exponent.
Take the given root of BOTH the numerator and denominator.

4. Simplify

5. Warm-up: Factional Radicands1) 2) 3)

6. How about….
BIG
NO NO!
When simplifying radicals, there can never be a radical left in the denominator of the final answer.
To get radicals out of the denominators, the denominator must be rationalized!
To rationalize the denominator, multiply the numerator and denominator by a radical that will make the denominators RADICAND a ‘perfect’ number.
LET’S SEE HOW THIS WORKS……………….

7. Rationalizing the Denominator
KEEP GOING…
Since the denominator is a square root, simply multiply the numerator and denominator by the radical in the denominator to give you a perfect square.
Simplify the numerator and denominator
BUT THERE IS STILL A RADICAL IN THE DENOMINATOR!

8. Rationalizing the Denominator
What do you notice about the denominator?
The radicand is now perfect!
Continue simplifying
Make sure each problem is simplified completely!
If the numbers outside the radical cannot be simplified… your DONE!

9. Try it yourself. Simplify the following.1)
How about with variables… 2)

10. Rationalizing Cube Roots
When rationalizing the denominator, always multiply the numerator and denominator by a radical that would make the radicand in the denominator perfect.
HINT: find a perfect number (according to the index) that is a multiple of the radicand.

11. Rationalizing Cube Roots

12. Rationalizing Cube Roots

13. Rationalizing Denominators

14. Rationalizing Binomial Denominator SOL: A2.2 and A2.3
Radicals
Rationalizing Binomial Denominator SOL: A2.2 and A2.3

15. Simplify
When radicals have binomial radicals in the denominator, multiply the numerator and denominator by the conjugate of the denominator to eliminate the radical in the denominator.
Simplify by distributing or using FOIL. then continue to completely simplify.
Be sure to simplify all numbers outside the radical if they all have common factors.

16. Rationalizing Binomial Radicals