Dividing Radical Expressions Section 8.5 Dividing Radical Expressions

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

Example Simplify. a. b.

Example Simplify. 75 can be simplified as

Example Simplify.

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.

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

Example Simplify.

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

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

Example Rationalize the denominator. The conjugate is