Question

Simplify the following by rationalizing the denominator.
$\frac{6-4\sqrt{2}}{6+4\sqrt{2}}$

Answer 1

Given

$\frac{6-4\sqrt{2}}{6+4\sqrt{2}}$

$=\frac{6-4\sqrt{2}}{6+4\sqrt{2}}\times \frac{6-4\sqrt{2}}{6-4\sqrt{2}}$

$=\frac{(6-4\sqrt{2}{)}^2}{(6{)}^2-(4\sqrt{2}{)}^2}$

$=\frac{36+16\times 2-48\sqrt{2}}{36-16\times 2}$

$=\frac{68-48\sqrt{2}}{4}$

$=\frac{4(17-12\sqrt{2})}{4}$

$=17-12\sqrt{2}$