Reduce the fraction $\frac{135}{3645}$ to lowest terms by extracting and canceling out $135$.
$$135\sqrt{\frac{1}{27}}$$
Rewrite the square root of the division $\sqrt{\frac{1}{27}}$ as the division of square roots $\frac{\sqrt{1}}{\sqrt{27}}$.
$$135\times \frac{\sqrt{1}}{\sqrt{27}}$$
Calculate the square root of $1$ and get $1$.
$$135\times \frac{1}{\sqrt{27}}$$
Factor $27=3^{2}\times 3$. Rewrite the square root of the product $\sqrt{3^{2}\times 3}$ as the product of square roots $\sqrt{3^{2}}\sqrt{3}$. Take the square root of $3^{2}$.
$$135\times \frac{1}{3\sqrt{3}}$$
Rationalize the denominator of $\frac{1}{3\sqrt{3}}$ by multiplying numerator and denominator by $\sqrt{3}$.
