Simplify the Radical Expression 4/(8- square root of 6)

$\frac{4}{8 - \sqrt{6}}$

Multiply $\frac{4}{8 - \sqrt{6}}$ by $\frac{8 + \sqrt{6}}{8 + \sqrt{6}}$ .

$\frac{4}{8 - \sqrt{6}} \cdot \frac{8 + \sqrt{6}}{8 + \sqrt{6}}$

Multiply $\frac{4}{8 - \sqrt{6}}$ by $\frac{8 + \sqrt{6}}{8 + \sqrt{6}}$ .

$\frac{4 (8 + \sqrt{6})}{(8 - \sqrt{6}) (8 + \sqrt{6})}$

Expand the denominator using the FOIL method.

$\frac{4 (8 + \sqrt{6})}{64 + 8 \sqrt{6} - 8 \sqrt{6} - {\sqrt{6}}^{2}}$

Simplify.

$\frac{4 (8 + \sqrt{6})}{58}$

Cancel the common factor of $4$ and $58$ .

Factor $2$ out of $4 (8 + \sqrt{6})$ .

$\frac{2 (2 (8 + \sqrt{6}))}{58}$

Cancel the common factors.

Factor $2$ out of $58$ .

$\frac{2 (2 (8 + \sqrt{6}))}{2 (29)}$

Cancel the common factor.

$\frac{2 (2 (8 + \sqrt{6}))}{2 \cdot 29}$

Rewrite the expression.

$\frac{2 (8 + \sqrt{6})}{29}$

The result can be shown in multiple forms.

Exact Form:

$\frac{2 (8 + \sqrt{6})}{29}$

Decimal Form:

$0.72065446 \dots$