Evaluate 4/(6- square root of 7)

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

Step 1

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

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

Step 2

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

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

Step 3

Expand the denominator using the FOIL method.

$\frac{4 (6 + \sqrt{7})}{36 + 6 \sqrt{7} - 6 \sqrt{7} - {\sqrt{7}}^{2}}$

Step 4

Simplify.

$\frac{4 (6 + \sqrt{7})}{29}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{4 (6 + \sqrt{7})}{29}$

Decimal Form:

$1.19251742 \dots$