This document provides instructions for dividing radicals and rationalizing denominators. It discusses simplifying coefficients and radicands when dividing radicals. When rationalizing denominators, it explains multiplying the numerator and denominator by a radical term called the conjugate to eliminate radicals in the denominator. The conjugate is formed by changing the sign of the second term of a binomial. Examples are provided to demonstrate rationalizing denominators using conjugates.

1. DIVIDING RADICALS
More Practice

2. DIVIDING RADICALS
 1) Simplify any coefficients
 2) Simplify the radicands, if possible
 3) Rationalize if necessary

3. REVIEW RATIONALIZING
 Rationalizing the denominator is a process by which is fraction is
rewritten so that the denominator only contains rational numbers (no
radicals).
 Create an equivalent fraction by multiplying the numerator and
denominator by a radical; create a perfect root in the denominator

4. PRACTICE

5. WHAT IF THERE IS MORE THAN ONE
TERM IN THE DENOMINATOR?

6. RATIONALIZING USING A CONJUGATE
 In algebra, the conjugate is a binomial formed by negating the second
term of a binomial.
 For example: the conjugate of (x+y) is (x-y), when x and y are Real
numbers
 If the numbers are imaginary, the process is called complex conjugation
 The complex conjugate of (a+bi) is (a-bi), where a and b are Real and “i”
is the imaginary number.

7. RATIONALIZING USING A CONJUGATE
 The conjugate of a denominator is the same expression but with a
different sign in the middle.
 This will allow terms with a radical to eliminate because of inverse
operations

8. RATIONALIZING USING A CONJUGATE
 1) Find the conjugate of the denominator
 2) Multiply the numerator and denominator by the conjugate (you will
have to FOIL the denominators)
 3) Simplify!

9. EXAMPLE:

3
5− 2

10. PRACTICE