How do you simplify 8/(3 + sqrt2)?

Jun 17, 2018

$\frac{1}{7} \left(24 - 8 \sqrt{2}\right)$

Explanation:

$\text{multiply the numerator/denominator by the "color(blue)"conjugate}$
$\text{of the denominator}$

$\text{the conjugate of "3+sqrt2" is } 3 \textcolor{red}{-} \sqrt{2}$

$= \frac{8 \left(3 - \sqrt{2}\right)}{\left(3 + \sqrt{2}\right) \left(3 - \sqrt{2}\right)}$

$= \frac{24 - 8 \sqrt{2}}{{3}^{2} - {\left(\sqrt{2}\right)}^{2}}$

$= \frac{24 - 8 \sqrt{2}}{7} = \frac{1}{7} \left(24 - 8 \sqrt{2}\right)$