How do you simplify #(sqrt10 + sqrt13)( sqrt10 - sqrt13)#?

1 Answer
Aron S.
Sep 17, 2015

#(sqrt(10) + sqrt(13))(sqrt(10) - sqrt(13)) = -3#

Explanation:

The two binomials in the expression are conjugates, as they have the form #(a+b)(a-b)#.

When you multiply two conjugates, you get the squares
#(a+b)(a-b) = (a^2-ab+ab+b^2) = (a^2-b^2)#

Applying this on the above expression, you get
#(sqrt(10) + sqrt(13))(sqrt(10) - sqrt(13)) = (sqrt(10)^2-sqrt(13)^2) = (10-13) = -3 #

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