Square Roots of a Quantity Squared An important

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Square Roots of a Quantity Squared • An important form of a square root

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

• 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

• 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 2 Simplify Table of Contents

• Example 3 Simplify Since x + 2 could be negative for certain

• 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

• 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

• 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,

• 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

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

• 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

• 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

Table of Contents

Table of Contents

Squares Square Roots Perfect Square Square Number AlsoSquares Square Roots Perfect Square Square Number Also
Perfect Square Roots Approximating NonPerfect Square Roots 8Perfect Square Roots Approximating NonPerfect Square Roots 8
Unit 2 SIMPLIFY SQUARE ROOTS Simplifying Square RootsUnit 2 SIMPLIFY SQUARE ROOTS Simplifying Square Roots
Square Roots and Solving Quadratics with Square RootsSquare Roots and Solving Quadratics with Square Roots
Square Roots 3 9 Finding Square Roots WarmSquare Roots 3 9 Finding Square Roots Warm
SIMPLIFYING SQUARE ROOTS Definition of radicals Square rootsSIMPLIFYING SQUARE ROOTS Definition of radicals Square roots
Square Roots 3 9 Finding Square Roots WarmSquare Roots 3 9 Finding Square Roots Warm
Square and Square Roots Cubes and Cube RootsSquare and Square Roots Cubes and Cube Roots
Chi Squared Test Why Chi Squared To testChi Squared Test Why Chi Squared To test
Squared coefficient of variation l The squared coefficientSquared coefficient of variation l The squared coefficient
Mean squared error MSE variance and bias squaredMean squared error MSE variance and bias squared