1. Dividing Radical Expressions
Section 8.5
Dividing Radical Expressions

2. Quotient Rule for Square Roots
For all positive numbers a and b,

3. Example
Simplify. a. b.

4. Example
Simplify.
75 can be simplified as

5. Example
Simplify.

6. Rationalizing Denominators
If a fraction has a radical in the denominator, the denominator needs to be rationalized. To rationalize a denominator, change the fraction to an equivalent one that has an integer in the denominator.

7. This will make a perfect square.
Example
Simplify.
This will make a perfect square.

8. Example
Simplify.

9. Conjugates
When the denominator of a fraction is a binomial with a square root, the denominator must be rationalized. This is done by using the conjugate of the denominator.
The conjugate of a binomial is a binomial having the same two terms with the sign of the second term changed.
The conjugate of
The conjugate of

10. Example
Simplify.
Multiply by the conjugate.
Distribute.
Simplify.

11. Example
Rationalize the denominator. The conjugate is