1. MAT 105 FALL 2008 Roots and Radicals
Section 1.6
Roots and Radicals

2. Square Roots
The principal square root is positive.

3. General Notation for Radicals
If n = 2, we do NOT write in the 2.
Thus, if no index is indicated, it is assumed to be 2 (square root).

4. Examples

5. The EVEN root of a negative number is a(n) _____________________ number.
The ODD root of a negative number is a _________________ _______ number.

6. A Property of Radicals
We will use this property to simplify radicals.

7. To Simplify Square Roots
Find a factor(s) of the radicand that is a perfect square.
Rewrite the radical as a product of square roots where at least one radicand is a perfect square, using the fact that
Simplify any radicals containing perfect squares.

8. Perfect Squares
When simplifying square roots, it is helpful to have handy a list of commonly used perfect squares (say, the first 15).

9. Examples

10. The property also holds for other indices.
Express the following in simplest radical form.

11. A similar property holds for division.
Express the following in simplest radical form.

12. WARNING!!! This property does NOT apply to addition or subtraction.
That is,
Remember to simplify under the radical first (FOLLOW ORDER OF OPERATIONS)!