Simplify 3/(4+ square root of 2)

$\frac{3}{4 + \sqrt{2}}$

Step 1

Multiply $\frac{3}{4 + \sqrt{2}}$ by $\frac{4 - \sqrt{2}}{4 - \sqrt{2}}$ .

$\frac{3}{4 + \sqrt{2}} \cdot \frac{4 - \sqrt{2}}{4 - \sqrt{2}}$

Step 2

Multiply $\frac{3}{4 + \sqrt{2}}$ by $\frac{4 - \sqrt{2}}{4 - \sqrt{2}}$ .

$\frac{3 (4 - \sqrt{2})}{(4 + \sqrt{2}) (4 - \sqrt{2})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{3 (4 - \sqrt{2})}{16 - 4 \sqrt{2} + \sqrt{2} \cdot 4 - {\sqrt{2}}^{2}}$

Step 4

Simplify.

$\frac{3 (4 - \sqrt{2})}{14}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{3 (4 - \sqrt{2})}{14}$

Decimal Form:

$0.55409709 \dots$