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