1. Chapter 8
Section 4

2. 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

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

4. 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

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

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

7. 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

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

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

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

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

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