Radical Expressions
11-9Multiplication of Binomials Containing Radicals
Overview
Multiply with FOIL; use (a − b)(a + b) = a² − b² to rationalize denominators.
Key ideas
- FOIL applies to radical binomials.
- Conjugates eliminate radicals from a denominator.
- Combine like radicals at the end.
Worked examples
Example 1
Problem. (√3 + 1)(√3 − 1)
Solution. 3 − 1 = 2
Example 2
Problem. (2 + √5)(2 − √5)
Solution. 4 − 5 = −1
Practice
Try each one. Click Show answer when ready.
- 1.
(√2 + 3)(√2 − 3)
- 2.
(√5 + 1)^2
- 3.
Rationalize 1/(√3 + 1).
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
Simplify (2 + √3)(5 − √3).
- 2.
Simplify (√5 + 2)².