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

Square Roots The principal square root is positive.

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).

Examples

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

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

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.

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

Examples

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

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

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