2. 6.2 Multiplying and Dividing
Radical Expressions

3. Simplest Form
• If the radicand of n a has a perfect nth power
among its factors, you can reduce the radical.
• If you reduce the radical as much as possible,
the radical is in simplest form.
– Always write your final answers in simplest form.

4. Example: Simplify
24

5. Example: Simplify
3
24

6. Example: Simplify, assume
variables are positive
3 5
54x

7. Combining Radical Expression: Products
• If a and b are real numbers, then
a × b = ab
n n
• If a and b are real numbers, then
n
a × n b = n ab

8. Example: Multiply, if possible. Then Simplify.
Assume variables are positive
3
−4 × 23

9. Example: Multiply, if possible. Then
Simplify. Assume variables are positive
72 x y × 10 xy
3 2 3

10. Example: Multiply, if possible. Then
Simplify. Assume variables are positive
45 x y × 35 xy
5 3 4

11. Combining Radical Expression: Products
• If a and b are real numbers and b≠0
a a
then =
b b
n
• If a and n
b are real numbers and
n
a na
then n =
b b

12. Example: Divide
18 x 5
2 x3

13. Example: Divide
5
3
162 y
2
3
3y

14. Rationalizing the Denominator
• To write a radical expression in simplest form,
we must eliminate radicals in the
denominators.
– The process of eliminating radicals in the
denominator is called rationalizing the
denominator

15. Rationalizing the Denominator
To rationalize the denominator
1. Simplify the radicals
2. Decide what you need to multiply by to make a
perfect power of n
3. Multiply the numerator and denominator
4. Simply

16. Example: Rationalize the denominator
1
2

17. Example: Rationalize the denominator
3
7x
2
3
5y

18. Example: Rationalize the denominator
3
5x2
3
12 y 2 z

19. Homework
• P 371 #12 – 51 multiples of 3