Simplify 1/( square root of 7+1)

$\frac{1}{\sqrt{7} + 1}$

Step 1

Multiply $\frac{1}{\sqrt{7} + 1}$ by $\frac{\sqrt{7} - 1}{\sqrt{7} - 1}$ .

$\frac{1}{\sqrt{7} + 1} \cdot \frac{\sqrt{7} - 1}{\sqrt{7} - 1}$

Step 2

Multiply $\frac{1}{\sqrt{7} + 1}$ by $\frac{\sqrt{7} - 1}{\sqrt{7} - 1}$ .

$\frac{\sqrt{7} - 1}{(\sqrt{7} + 1) (\sqrt{7} - 1)}$

Step 3

Expand the denominator using the FOIL method.

$\frac{\sqrt{7} - 1}{{\sqrt{7}}^{2} + \sqrt{7} \cdot - 1 + \sqrt{7} - 1}$

Step 4

Simplify.

$\frac{\sqrt{7} - 1}{6}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{7} - 1}{6}$

Decimal Form:

$0.27429188 \dots$