7. Roots and Radical Expressions

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Presentation transcript:

7. Roots and Radical Expressions

Real Roots Real roots are the possible solutions to a number, raised to a power.

Vocabulary and Properties Radical sign index radicand

How to find the root (other than a square root), using a graphing calculator 1. Input the root you are going to take (for example, if you are taking the third root of a number, start with the 3). 2. Press MATH and select option 5 3. Enter the value you are taking the root of. Ex: 4 MATH 5 81 ENTER 3

Practice: Find each root Solutions: 22, 7, and ERR: NONREAL ANS Let’s take a closer look at this answer

Properties and Notation: Why? We want to make sure that the root is always positive when the index is an even number When n is an even number

Note: Absolute value symbols ensure that the root is positive when x is negative. They are not needed for y because y2 is never negative. Notice that the index is an odd number here . . . Absolute value symbols must not be used here. If x is negative, then the radicand is negative and the root must also be negative.

Let’s try some Simplify each expression. Use the absolute value symbols when needed.

Fractional Exponents (Powers and Roots)

RADICAL TO EXPONENT RULE

RATIONAL EXPONENT RULE