1. Roots of Real Numbers and Radical Expressions

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

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

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

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

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

7. Examples

8. Examples

9. Taking nth roots of variable expressions Using absolute value signs
If the index (n) of the radical is even, the power under the radical sign is even, and the resulting power is odd, then we must use an absolute value sign.

10. Examples
Even
Odd
Even
Odd

11. Even 2
Odd
Odd
Even