Chapter 8 Section 4

Rationalizing the Denominator 8.4 Rationalizing the Denominator Rationalize denominators with square roots. Write radicals in simplified form. Rationalize denominators with cube roots. 2 3

Rationalize denominators with square roots. Objective 1 Rationalize denominators with square roots. Slide 8.4-3

Rationalize denominators with square roots. It is easier to work with a radical expression if the denominators do not contain any radicals. This process of changing the denominator from a radical, or irrational number, to a rational number is called rationalizing the denominator. The value of the radical expression is not changed; only the form is changed, because the expression has been multiplied by 1 in the form of Slide 8.4-4

Rationalizing Denominators EXAMPLE 1 Rationalizing Denominators Rationalize each denominator. Solution: Slide 8.4-5

Write radicals in simplified form. Objective 2 Write radicals in simplified form. Slide 8.4-6

Write radicals in simplified form. Conditions for Simplified Form of a Radical 1. The radicand contains no factor (except 1) that is a perfect square (in dealing with square roots), a perfect cube (in dealing with cube roots), and so on. 2. The radicand has no fractions. 3. No denominator contains a radical. Slide 8.4-7

EXAMPLE 2 Simplifying a Radical Simplify Solution: Slide 8.4-8

Simplifying a Product of Radicals EXAMPLE 3 Simplifying a Product of Radicals Simplify Solution: Slide 8.4-9

Simplifying Quotients Involving Radicals EXAMPLE 4 Simplifying Quotients Involving Radicals Simplify. Assume that p and q are positive numbers. Solution: Slide 8.4-10

Rationalize denominators with cube roots. Objective 3 Rationalize denominators with cube roots. Slide 8.4-11

Rationalizing Denominators with Cube Roots EXAMPLE 5 Rationalizing Denominators with Cube Roots Rationalize each denominator. Solution: Slide 8.4-12