1. Square Roots
a is a square root of b if and only if
Example 1
3 is a square root of 9, since
- 3 is also a square root of 9, since
Thus, 9 has two square roots, -3 and 3.

2. Example 2
The number 0 has only one square root, which is 0 since

3. Sometimes there are no square roots of a number.
Example 3:
There are no square roots of –16 since there are no numbers a such that
Note that neither 4 nor – 4 will work.

4. Radical notation
Radical symbol
Square root of a
The expression that appears under the radical sign, a in this case, is called the radicand.
When radical notation is used, the result is the principal square root, which is the non-negative root.

5. Example 4
Simplify:
There are two square roots of 25, - 5 and 5.
The principal second root is the non-negative root, or 5. Therefore,

6. Example 5
Simplify
Reasoning
Note that while it is also true that
we want the principal (nonnegative) root.

7. Example 6
Simplify
Reasoning

8. Example 7
Simplify
Reasoning
is undefined.

9. Example 8
Simplify
Reasoning

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END OF PRESENTATION
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