Evaluate 5/(7- square root of 2)

$\frac{5}{7 - \sqrt{2}}$

Step 1

Multiply $\frac{5}{7 - \sqrt{2}}$ by $\frac{7 + \sqrt{2}}{7 + \sqrt{2}}$ .

$\frac{5}{7 - \sqrt{2}} \cdot \frac{7 + \sqrt{2}}{7 + \sqrt{2}}$

Step 2

Multiply $\frac{5}{7 - \sqrt{2}}$ by $\frac{7 + \sqrt{2}}{7 + \sqrt{2}}$ .

$\frac{5 (7 + \sqrt{2})}{(7 - \sqrt{2}) (7 + \sqrt{2})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{5 (7 + \sqrt{2})}{49 + 7 \sqrt{2} - 7 \sqrt{2} - {\sqrt{2}}^{2}}$

Step 4

Simplify.

$\frac{5 (7 + \sqrt{2})}{47}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{5 (7 + \sqrt{2})}{47}$

Decimal Form:

$0.89512910 \dots$