1. Radical Functions
Unit 3

2. Parts of a Radical
index
radical
𝑛 𝑚
radican

3. Radicals Principal root—positive root (for even indexes)
For a radical to be completely simplified,
(A) all perfect nth root factors should be
removed from underneath the radical,
(B) no fractions left underneath the radical, and
(C) no radicals left in the denominator
All even powered variables are perfect squares— the square root is the ½ power.

4. Simplify, if possible

5. Simplify, if possible

6. Simplify, if possible

7. Simplify, if possible

8. Rationalizing the denominator
Multiply by a sq. rt. that will give you a perfect sq. in the denominator so that you can eliminate the radical

9. Simplify, if possible

10. Simplifying Higher Order Radicals
3 54 𝑥 5
3 162 𝑥 5

11. Simplify
3 −27 𝑥 7 𝑦 5 𝑧 6
5 −64 𝑓 6 𝑔 5 ℎ 27

12. Examples

13. More Examples

14. Radical Operations +, -, X, / Radicals Treat Radicals like variables
Must have like radicals to add or subtract
Like radicals are the same radicand and the same index

15. More Radical Operations
When multiplying— remember “inside #s with inside #s and outside #s with outside #s”
Multiply then simplify or simplify then multiply
You must foil if you multiply a binomial by another binomial!!

16. Dividing Radicals
When dividing, you can not have a radical left in the denominator in the final answer. If there is only 1 term, then we rationalize. If there are 2 terms, then multiply by the conjugate

17. Examples

18. Simplify completely