# How would you simplify (sqrt13 - sqrt3) ( sqrt13 + sqrt 3)?

Feb 24, 2016

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

#### Explanation:

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

This is an example of the difference of squares, ${a}^{2} - {b}^{2} = \left(a + b\right) \left(a - b\right)$, where $a = \sqrt{13}$ and $b = \sqrt{3}$.

Rewrite the expression as a difference of squares.

${\sqrt{13}}^{2} - {\sqrt{3}}^{2}$

Apply the square root rule ${\sqrt{a}}^{2} = a$.

$13 - 3$

Simplify.

$10$