Simplify 2/( square root of 5+1)

$\frac{2}{\sqrt{5 + 1}}$

Add $5$ and $1$ .

$\frac{2}{\sqrt{6}}$

Multiply $\frac{2}{\sqrt{6}}$ by $\frac{\sqrt{6}}{\sqrt{6}}$ .

$\frac{2}{\sqrt{6}} \cdot \frac{\sqrt{6}}{\sqrt{6}}$

Combine and simplify the denominator.

Multiply $\frac{2}{\sqrt{6}}$ by $\frac{\sqrt{6}}{\sqrt{6}}$ .

$\frac{2 \sqrt{6}}{\sqrt{6} \sqrt{6}}$

Raise $\sqrt{6}$ to the power of $1$ .

$\frac{2 \sqrt{6}}{{\sqrt{6}}^{1} \sqrt{6}}$

Raise $\sqrt{6}$ to the power of $1$ .

$\frac{2 \sqrt{6}}{{\sqrt{6}}^{1} {\sqrt{6}}^{1}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{2 \sqrt{6}}{{\sqrt{6}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{2 \sqrt{6}}{{\sqrt{6}}^{2}}$

Rewrite ${\sqrt{6}}^{2}$ as $6$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{6}$ as $6^{\frac{1}{2}}$ .

$\frac{2 \sqrt{6}}{{(6^{\frac{1}{2}})}^{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{2 \sqrt{6}}{6^{\frac{1}{2} \cdot 2}}$

Combine $\frac{1}{2}$ and $2$ .

$\frac{2 \sqrt{6}}{6^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 \sqrt{6}}{6^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{2 \sqrt{6}}{6^{1}}$

Evaluate the exponent.

$\frac{2 \sqrt{6}}{6}$

Cancel the common factor of $2$ and $6$ .

Factor $2$ out of $2 \sqrt{6}$ .

$\frac{2 (\sqrt{6})}{6}$

Cancel the common factors.

Factor $2$ out of $6$ .

$\frac{2 \sqrt{6}}{2 \cdot 3}$

Cancel the common factor.

$\frac{2 \sqrt{6}}{2 \cdot 3}$

Rewrite the expression.

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.81649658 \dots$