Find the square root of $\dfrac{507}{4107}$.

$\sqrt{\dfrac{507}{4107}}\\[1em] = \sqrt{\dfrac{169}{1369}}\\[1em] = {\dfrac{\sqrt{169}}{\sqrt{1369}}}\\[1em] = {\dfrac{13}{37}}$

Square root of 169 using division method:

$\sqrt{169} = 13$

Square root of 1369 using division method:

$\sqrt{1369} = 37$

$\therefore {\dfrac{\sqrt{169}}{\sqrt{1369}}} = {\dfrac{13}{37}}$

$\sqrt{\dfrac{507}{4107}} = {\dfrac{13}{37}}$