Question

Rational the denominator & simplify:-
$\frac{6-4\sqrt{2}}{6+4\sqrt{2}}$

Answer 1

Rationalizing the denominator of $\frac{6-4\sqrt{2}}{6+4\sqrt{2}}$.

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

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

$=\frac{36-32-48\sqrt{2}}{36-32}$

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

$=\frac{4\left(1-12\sqrt{2}\right)}{4}$

$=1-12\sqrt{2}$