Square Roots of a Quantity Squared An important

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 1 Note 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. Since is always nonnegative, the absolute value sign is not necessary. Table of Contents

• Example 5 Simplify First write the radicand as a quantity squared. Since would 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 4 x - 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. Table of Contents

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