Rationalize the Denominator 3/(6- square root of 2)${\displaystyle \frac{3}{6-\sqrt{2}}}$

Rationalize the Denominator 3/(6- square root of 2)${\displaystyle \frac{3}{6-\sqrt{2}}}$

Multiply${\displaystyle \frac{3}{6-\sqrt{2}}}$ by ${\displaystyle \frac{6+\sqrt{2}}{6+\sqrt{2}}}$.

${\displaystyle \frac{3}{6-\sqrt{2}}\cdot \frac{6+\sqrt{2}}{6+\sqrt{2}}}$

Multiply${\displaystyle \frac{3}{6-\sqrt{2}}}$ and ${\displaystyle \frac{6+\sqrt{2}}{6+\sqrt{2}}}$.

${\displaystyle \frac{3(6+\sqrt{2})}{(6-\sqrt{2})(6+\sqrt{2})}}$

Expand the denominator using the FOIL method.

${\displaystyle \frac{3(6+\sqrt{2})}{36+6\sqrt{2}-6\sqrt{2}-{\sqrt{2}}^{2}}}$

Simplify.

${\displaystyle \frac{3(6+\sqrt{2})}{34}}$

The result can be shown in multiple forms.

Exact Form:

${\displaystyle \frac{3(6+\sqrt{2})}{34}}$

Decimal Form:

${\displaystyle 0.65419531\dots }$