Expanding Square Roots

Question

Expand (√5 + 2√3)(√5 -2√3). Express your answer as simply as possible.

 

Please explain how to answer this question. Thanks :)

Answer 1

If you look closely, you can see that this problem is the the factored version of a difference of two squares. FOIL out the multiplication as you would any other multiplication of binomials and then simplify. 

Answer 2

This problem is an application of the "difference of squares".  For any two numbers, a and b:

 

(a+b)(a-b) = a² - b²

 

You can prove this yourself by multiplying (a+b)(a-b) using the FOIL or box methods.  In your problem, a = √5 and b = 2√3.  Hence:

 

(√5 + 2√3)(√5 - 2√3) = (√5)² - (2√3)² = 5 - 4*3 = -7