Simplify the Radical Expression 7/(3- square root of 2)

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

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

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

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

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

Expand the denominator using the FOIL method.

$\frac{7 (3 + \sqrt{2})}{9 + 3 \sqrt{2} - 3 \sqrt{2} - {\sqrt{2}}^{2}}$

Simplify.

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

Cancel the common factor of $7$ .

Cancel the common factor.

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

Divide $3 + \sqrt{2}$ by $1$ .

$3 + \sqrt{2}$

The result can be shown in multiple forms.

Exact Form:

$3 + \sqrt{2}$

Decimal Form:

$4.41421356 \dots$