How do you simplify (5+sqrt3)(5-sqrt3)?

Jun 5, 2015

This is of the form $\left(a + b\right) \left(a - b\right)$ with $a = 5$ and $b = \sqrt{3}$

$\left(a + b\right) \left(a - b\right) = {a}^{2} - {b}^{2}$

So

$\left(5 + \sqrt{3}\right) \left(5 - \sqrt{3}\right) = {5}^{2} - {\left(\sqrt{3}\right)}^{2} = 25 - 3 = 22$