1. Radicals

2. Radicals

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

4. Examples

5. More

6. More Examples

7. Rationalizing the denominator
Multiply by a root that will give you a perfect nth root in the denominator in order to eliminate the radical

8. 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

9. 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!!

10. 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

11. Examples