Table of Contents 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.

Table of Contents Example 1Note the patterns here. Same Opposite in sign

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

Table of Contents Example 2 Simplify

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

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

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

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

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

Table of Contents 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.

Table of Contents 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.

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