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

Sep 17, 2015

$\left(\sqrt{10} + \sqrt{13}\right) \left(\sqrt{10} - \sqrt{13}\right) = - 3$

#### Explanation:

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

When you multiply two conjugates, you get the squares
$\left(a + b\right) \left(a - b\right) = \left({a}^{2} - a b + a b + {b}^{2}\right) = \left({a}^{2} - {b}^{2}\right)$

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