7.3 – binomial radical expressions. i. adding and subtracting radical expressions like radicals...
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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