     Home Real Numbers Radicals Inequalities & Absolute Value Polynomials Rational Expressions 1 Rat'l. Exp. 2 - mult&div Rat'l. Exp. 3 - add&subt Slope & Equations of Lines Review&Test ### UNIT 1  : PRECALCULUS PREP

LESSON 2:  REAL NUMBERS - RADICALS NOTE:  Each of these examples is an irrational real number. Example 1: Example 2:  Write as mixed radicals.    Solutions:     Example 3:  Write as entire radicals.    Solutions:    Example 4:  Simplify    Solutions:    Examples:

2x – 3y + 5x – 6y = 2x + 5x – 3y – 6y = 7x – 9y

Similarly Example 5:  Simplify   Solutions:   Example 6:  Simplify    Solutions:

Again we follow the rules of ordinary algebra for expanding  Recall from ordinary algebra the product of two binomials:

(x + 3)(x + 5) = x(x + 5) + 3(x + 5)

= x2 + 5x + 3x + 15

= x2 + 8x + 15   Recall all of the properties of radicals mentioned above: Example 7:  Simplify Division of Radicals with Irrational denominators:  Examples: These are simplified by a process called rationalizing the denominator.

Example 8:  Simplify by rationalizing the denominator. Example 9:  Simplify Example 10: Simplify Example 11: Simplify 