Factor $63=3^{2}\times 7$. Rewrite the square root of the product $\sqrt{3^{2}\times 7}$ as the product of square roots $\sqrt{3^{2}}\sqrt{7}$. Take the square root of $3^{2}$.
$$\frac{\sqrt{21}\times 3}{3\sqrt{7}}$$
Cancel out $3$ in both numerator and denominator.
$$\frac{\sqrt{21}}{\sqrt{7}}$$
Rewrite the division of square roots $\frac{\sqrt{21}}{\sqrt{7}}$ as the square root of the division $\sqrt{\frac{21}{7}}$ and perform the division.
