1. Radicals and Radical Functions
13.3
Radicals and Radical Functions

2. Square Roots
Opposite of squaring a number is taking the square root of a number.
A number b is a square root of a number a if b2 = a.
In order to find a square root of a, you need a number that, when squared, equals a.

3. Radicands _________________is an expression containing a ___________.
____________ is the expression under a radical sign.
Note that if the radicand of a square root is a negative number, the radical is NOT a real number.

4. Principal Square Roots
Principal and Negative Square Roots
If a is a nonnegative number, then
is the principal or nonnegative square root of a
is the negative square root of a.

5. Example
Find each square root. a. b. c. d.

6. Example
Find each cube root. a. b. c. d.

7. nth Roots Other roots can be found, as well.
The nth root of a is defined as
If the index, n, is even, the root is NOT a real number when a is negative.
If the index is odd, the root will be a real number.

8. Example
Find each root. a. b. c.