How do you simplify # (sqrt2 + sqrt6)(sqrt2 - sqrt6)#?

2 Answers
Jun 2, 2016

Answer:

The result is -4.

Explanation:

When you multiply two numbers in the form #(A+B)(A-B)# you obtain as result #A^2-B^2#.

In your case #A=sqrt(2)# and #B=sqrt(6)# then

#(sqrt(2)+sqrt(6))(sqrt(2)-sqrt(6))=sqrt(2)^2-sqrt(6)^2=2-6=-4#.

Jun 2, 2016

Answer:

#2 - 6 = -4#

Explanation:

This is in the same format as #(x + y)(x - y)# which are the factors of #x^2 - y^2, " known as the difference between two squares"#

So if #(x + y)(x - y) = x^2 - y^2#, then

#(sqrt2 + sqrt6)(sqrt2 - sqrt6) = (sqrt2)^2 - (sqrt6)^2#

This simplifies to #2 - 6 = -4#

This could also be simplified by multiplying out the brackets to get 4 terms, but the answer will be the same - it will just take longer.