How do you simplify open parentheses 5 plus square root of 3 close parentheses open parentheses 5 minus square root of 3 close parentheses?

Mar 5, 2018

22

Explanation:

$\left(5 + \sqrt{3}\right) \left(5 - \sqrt{3}\right)$

$= 5 \left(5 - \sqrt{3}\right) + \sqrt{3} \left(5 - \sqrt{3}\right)$

$= 25 - 5 \sqrt{3} + 5 \sqrt{3} - 3$

$= 25 - 3$

$= 22$

Note: given the identity that
$\left(x + y\right) \left(x - y\right) = {x}^{2} - {y}^{2}$

$\left(5 + \sqrt{3}\right) \left(5 - \sqrt{3}\right)$

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

$= 22$