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

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Answer 1 · 2015-09-17T18:00:34

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

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
$(sqrt(10) + sqrt(13))(sqrt(10) - sqrt(13)) = (sqrt(10)^2-sqrt(13)^2) = (10-13) = -3$

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