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.

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Presentation transcript:

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.

Example 1Note the patterns here. Same Opposite in sign

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

Example 2 Simplify

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

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

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

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

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

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.

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.