Simplify 5/(3+ square root of 6)

$\frac{5}{3 + \sqrt{6}}$

Step 1

Multiply $\frac{5}{3 + \sqrt{6}}$ by $\frac{3 - \sqrt{6}}{3 - \sqrt{6}}$ .

$\frac{5}{3 + \sqrt{6}} \cdot \frac{3 - \sqrt{6}}{3 - \sqrt{6}}$

Step 2

Multiply $\frac{5}{3 + \sqrt{6}}$ by $\frac{3 - \sqrt{6}}{3 - \sqrt{6}}$ .

$\frac{5 (3 - \sqrt{6})}{(3 + \sqrt{6}) (3 - \sqrt{6})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{5 (3 - \sqrt{6})}{9 - 3 \sqrt{6} + \sqrt{6} \cdot 3 - {\sqrt{6}}^{2}}$

Step 4

Simplify.

$\frac{5 (3 - \sqrt{6})}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{5 (3 - \sqrt{6})}{3}$

Decimal Form:

$0.91751709 \dots$