1. TOPIC 18.1 Radical Expressions

2. OBJECTIVES Find Square Roots of Perfect Squares
Approximate Square Roots
Simplify Radical Expressions of the Form
Find Cube Roots
Find and Approximate th Roots

3. Definitions Principal Square Root: Negative Square Root:
A non-negative real number is the principal square root of a non-negative real number denoted as
Negative Square Root:
A negative real number is the negative square root of a non-negative real number denoted as
Radical Expression: an expression that contains a radical sign
The expression beneath the radical sign is called the radicand.
Cube Root:
A real number is the cube root of a real number denoted as
Principal th Roots:

4. Simplifying Radicals Simplifying Radical Expressions of the Form
For any real number
If is an integer such that is a real number, then

5. Approximating Square Roots
A square root simplifies to a rational number if the radicand is a perfect square.
When the radicand is not a perfect square, the square root is an irrational number.
For such radical expressions, we can find decimal approximations using a calculator.
Before doing this, consider what might be a reasonable result.
Example: Approximate
Notice that is between the perfect squares Thus, the principal square root of should be between the principal square roots of
Enter into the calculator.

6. Examples
We need to find the negative square root of Since
Evaluate

7. Find Cube Roots
One can apply the process of finding square roots to other types of roots.
Recall that the cube of a negative number is a negative number. Unlike square roots, cube roots can have negative numbers in the radicand.
Every real number has one real cube root. If the radicand is positive, the cube root will be positive. If the radicand is negative, the cube root will be negative.
Example:

8. Find nth Route
In the notation is called the index of the radical expression, and it indicates the type of root.
For example, a cube root has an index of If no index is shown, then it is understood to be for a square root.
Example:
Simplify