1. Square Roots of a Quantity Squared An important form of a square root is: It would seem that we should write … … but as we shall see, this is not always the case.

2. Example 1Note the patterns here. Same Opposite in sign

3. Recall that the absolute value of a negative number is the opposite of that number. We now define …

4. Example 2 Simplify

5. Example 3 Simplify Since x + 2 could be negative for certain values of x, we must keep the absolute value sign.

6. Example 4 Simplify First write the radicand as a quantity squared. Sinceis always nonnegative, the absolute value sign is not necessary.

7. Example 5 Simplify First write the radicand as a quantity squared. Sincewould be negative if a were negative, the absolute value sign is necessary.

8. Example 6 Simplify Try to create the pattern of To do this, factor the radicand.

9. Since 4x - 5 could be negative for certain values of x, we must keep the absolute value sign.

10. Sometimes the directions will include a statement that the values of the variables will be such that the radicand will be nonnegative. In this case, the absolute value sign is not necessary.

11. Example 7 Simplify the expression, assuming that the variable represents a nonnegative value. Since the variable can’t be negative, the absolute value sign is not necessary.