Entry Task– Simplify Expand then solve 3 5, 3 4, 3 3, 3 2 and 3 1 on a separate line in your notebook Now do 3 -1, 3 -2, 3 -3, 3 -4 and 3 -5 but leave a line between the positive and neagtive

6.1 Roots and Radical Expressions Learning Target: I can find the nth root

Definition of n th Root ** For a square root the value of n is 2. For any real numbers a and b and any positive integers n, if a n = b, then a is an nth root of b.

Notation index radical radicand Note: An index of 2 is understood but not written in a square root sign.

Principal Root The nonnegative root of a number Principal square root Opposite of principal square root Both square roots

Summary of Roots even odd one + root one - root one + root no - roots no real roots no + roots one - root one real root, 0

Simplify To simplify means to find x in the equation: x 4 = 81 Solution: = 3

-20.6 Example 1: Evaluating N th roots Simplify each of the following roots. – Click each expression to reveal the answer. ±13 No real root

Examples

Assignment pg 364 #10,12,14,16,18,19,21,23-34 all A review of the properties of exponents are on the following slides…..

Properties of Exponents – let’s review...

NEGATIVE EXPONENT RULE

PRODUCT OR POWER RULE HAVE TO HAVE THE SAME BASE

QUOTIENT OF POWER RULE HAVE TO HAVE THE SAME BASE

POWER OF POWER RULE ( x 4 )³

POWER OF PRODUCT RULE ( 2x 4 ) ⁵

POWER OF A QUOTIENT RULE

POWER OF QUOTIENT 2 RULE

Fractional Exponents (Powers and Roots) “Power” “Root”

RADICAL TO EXPONENT RULE

RATIONAL EXPONENT RULE