Simplify 3/(7- square root of 2)

$\frac{3}{7 - \sqrt{2}}$

Multiply $\frac{3}{7 - \sqrt{2}}$ by $\frac{7 + \sqrt{2}}{7 + \sqrt{2}}$ .

$\frac{3}{7 - \sqrt{2}} \cdot \frac{7 + \sqrt{2}}{7 + \sqrt{2}}$

Multiply $\frac{3}{7 - \sqrt{2}}$ and $\frac{7 + \sqrt{2}}{7 + \sqrt{2}}$ .

$\frac{3 (7 + \sqrt{2})}{(7 - \sqrt{2}) (7 + \sqrt{2})}$

Expand the denominator using the FOIL method.

$\frac{3 (7 + \sqrt{2})}{49 + 7 \sqrt{2} - 7 \sqrt{2} - {\sqrt{2}}^{2}}$

Simplify.

$\frac{3 (7 + \sqrt{2})}{47}$

The result can be shown in multiple forms.

Exact Form:

$\frac{3 (7 + \sqrt{2})}{47}$

Decimal Form:

$0.53707746 \dots$

Simplify 3/(7- square root of 2)