Evaluate square root of 6/19

$\sqrt{\frac{6}{19}}$

Step 1

Rewrite $\sqrt{\frac{6}{19}}$ as $\frac{\sqrt{6}}{\sqrt{19}}$ .

$\frac{\sqrt{6}}{\sqrt{19}}$

Step 2

Multiply $\frac{\sqrt{6}}{\sqrt{19}}$ by $\frac{\sqrt{19}}{\sqrt{19}}$ .

$\frac{\sqrt{6}}{\sqrt{19}} \cdot \frac{\sqrt{19}}{\sqrt{19}}$

Step 3

Combine and simplify the denominator.

Multiply $\frac{\sqrt{6}}{\sqrt{19}}$ by $\frac{\sqrt{19}}{\sqrt{19}}$ .

$\frac{\sqrt{6} \sqrt{19}}{\sqrt{19} \sqrt{19}}$

Raise $\sqrt{19}$ to the power of $1$ .

$\frac{\sqrt{6} \sqrt{19}}{{\sqrt{19}}^{1} \sqrt{19}}$

Raise $\sqrt{19}$ to the power of $1$ .

$\frac{\sqrt{6} \sqrt{19}}{{\sqrt{19}}^{1} {\sqrt{19}}^{1}}$

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

$\frac{\sqrt{6} \sqrt{19}}{{\sqrt{19}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{\sqrt{6} \sqrt{19}}{{\sqrt{19}}^{2}}$

Rewrite ${\sqrt{19}}^{2}$ as $19$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{19}$ as $19^{\frac{1}{2}}$ .

$\frac{\sqrt{6} \sqrt{19}}{{(19^{\frac{1}{2}})}^{2}}$

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

$\frac{\sqrt{6} \sqrt{19}}{19^{\frac{1}{2} \cdot 2}}$

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

$\frac{\sqrt{6} \sqrt{19}}{19^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{\sqrt{6} \sqrt{19}}{19^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{\sqrt{6} \sqrt{19}}{19^{1}}$

Evaluate the exponent.

$\frac{\sqrt{6} \sqrt{19}}{19}$

Step 4

Simplify the numerator.

Combine using the product rule for radicals.

$\frac{\sqrt{6 \cdot 19}}{19}$

Multiply $6$ by $19$ .

$\frac{\sqrt{114}}{19}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{114}}{19}$

Decimal Form:

$0.56195148 \dots$