7.3 – Binomial Radical Expressions

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

Simplify Radicals Before Adding or Subtracting

Example 1: add or subtract the following

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

Example 2: multiply the following

A) (8 + 2√3)(3 - 3√3)

B) (√3 + √5)(√4 + √3)

C) (2 + √3)(2 - √3)

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

Example 3: Simplify the following