Evaluate 4/(7- square root of 6)

$\frac{4}{7 - \sqrt{6}}$

Step 1

Multiply $\frac{4}{7 - \sqrt{6}}$ by $\frac{7 + \sqrt{6}}{7 + \sqrt{6}}$ .

$\frac{4}{7 - \sqrt{6}} \cdot \frac{7 + \sqrt{6}}{7 + \sqrt{6}}$

Step 2

Multiply $\frac{4}{7 - \sqrt{6}}$ by $\frac{7 + \sqrt{6}}{7 + \sqrt{6}}$ .

$\frac{4 (7 + \sqrt{6})}{(7 - \sqrt{6}) (7 + \sqrt{6})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{4 (7 + \sqrt{6})}{49 + 7 \sqrt{6} - 7 \sqrt{6} - {\sqrt{6}}^{2}}$

Step 4

Simplify.

$\frac{4 (7 + \sqrt{6})}{43}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{4 (7 + \sqrt{6})}{43}$

Decimal Form:

$0.87902230 \dots$