Evaluate square root of 2/13

$\sqrt{\frac{2}{13}}$

Step 1

Rewrite $\sqrt{\frac{2}{13}}$ as $\frac{\sqrt{2}}{\sqrt{13}}$ .

$\frac{\sqrt{2}}{\sqrt{13}}$

Step 2

Multiply $\frac{\sqrt{2}}{\sqrt{13}}$ by $\frac{\sqrt{13}}{\sqrt{13}}$ .

$\frac{\sqrt{2}}{\sqrt{13}} \cdot \frac{\sqrt{13}}{\sqrt{13}}$

Step 3

Combine and simplify the denominator.

Multiply $\frac{\sqrt{2}}{\sqrt{13}}$ by $\frac{\sqrt{13}}{\sqrt{13}}$ .

$\frac{\sqrt{2} \sqrt{13}}{\sqrt{13} \sqrt{13}}$

Raise $\sqrt{13}$ to the power of $1$ .

$\frac{\sqrt{2} \sqrt{13}}{{\sqrt{13}}^{1} \sqrt{13}}$

Raise $\sqrt{13}$ to the power of $1$ .

$\frac{\sqrt{2} \sqrt{13}}{{\sqrt{13}}^{1} {\sqrt{13}}^{1}}$

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

$\frac{\sqrt{2} \sqrt{13}}{{\sqrt{13}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{\sqrt{2} \sqrt{13}}{{\sqrt{13}}^{2}}$

Rewrite ${\sqrt{13}}^{2}$ as $13$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{13}$ as $13^{\frac{1}{2}}$ .

$\frac{\sqrt{2} \sqrt{13}}{{(13^{\frac{1}{2}})}^{2}}$

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

$\frac{\sqrt{2} \sqrt{13}}{13^{\frac{1}{2} \cdot 2}}$

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

$\frac{\sqrt{2} \sqrt{13}}{13^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{\sqrt{2} \sqrt{13}}{13^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{\sqrt{2} \sqrt{13}}{13^{1}}$

Evaluate the exponent.

$\frac{\sqrt{2} \sqrt{13}}{13}$

Step 4

Simplify the numerator.

Combine using the product rule for radicals.

$\frac{\sqrt{2 \cdot 13}}{13}$

Multiply $2$ by $13$ .

$\frac{\sqrt{26}}{13}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{26}}{13}$

Decimal Form:

$0.39223227 \dots$