1. 7.3 – Binomial Radical Expressions

2. I. Adding and Subtracting Radical Expressions  Like Radicals – radicals that have the same radicand and index.  When adding or subtracting radical expressions, treat like adding/subtracting variables.  Only combine number in front of radical and keep radical the same, unless you can simplify!  You need to have like radicals in order to combine. For Example: 3√x + 23√x = 33√x

3.  Simplify Radicals Before Adding or Subtracting  Example 1: add or subtract the following

4. II. Multiplying and Dividing Radicals  When multiplying radicals, use the FOIL method, then simplify For Example; (2 + 2√5)(4 + 6√5) 8 + 12√5 + 8√5 + 12√25 8 + 20√5 + 12(5) 8 + 60 + 20√5 68 + 20√5

5.  Example 2: multiply the following A) (8 + 2√3)(3 - 3√3) B) (√3 + √5)(√4 + √3) C) (2 + √3)(2 - √3)

6. II. Simplifying Rational Radical Expressions  You may need rationalize the denominator by multiplying by the denominator’s conjugate.  NO RADICALS ARE TO BE IN THE DONOMINATOR

7.  Example 3: Simplify the following