1. Roots & Radical Expressions
NOTES 7.1
Roots & Radical Expressions

2. Definitions/Key Concepts
52 _______, 5 is a ________ root of 25
53 _______, 5 is a ________ root of 125
54 _______, 5 is a ________ root of 625
Definition of nth root for REAL NUMBERS:
an = b means a is the nth root of b 25
square
125
cube
625
fourth

3. Summary of Possible Real Roots
Type of
Number
# of REAL nth roots,
when n is even
when n is odd
Positive 2 1
Negative
EXAMPLE: Find All Real Roots
The cube root of 27 = _______
The fourth root of 81 = _______
The sixth root of -64 = ________ 3
The cube root of -8/27 = _______
The fourth root of 16/81 = _______
The cube root of = ________
-2/3
± 3
± 2/3
No real roots
0.2

4. Radical Signs! You can use a radical sign to indicate the root.
The Index gives the degree of the root.
The radicand is the number under the radical sign.

5. Steps To Finding Real Roots
Step 1: Deal with the NUMBERS first (if any). Use calculator as necessary.
Step 2: With Variables Inside the Radicand: You can just divide the exponent by the INDEX. The whole number comes out of the radical, and the remainder (if any) stays inside the radical.
Step 2: Simplify the Expression
Example:
9x10
IMPORTANT NOTE: ONLY USE ABSOLUTE VALUE SYMBOLS
WHEN THE INDEX IS EVEN AND THE SIMPLIFIED EXPRESSION
CONTAINS A VARIABLE WITH AN ODD DEGREE

6. Important Property

7. Additional Examples