Rewrite the square root of the division $\frac{49}{16}$ as the division of square roots $\frac{\sqrt{49}}{\sqrt{16}}$. Take the square root of both numerator and denominator.
$$\frac{\frac{7}{4}}{\sqrt{\frac{2400}{784}}}$$
Reduce the fraction $\frac{2400}{784}$ to lowest terms by extracting and canceling out $16$.
$$\frac{\frac{7}{4}}{\sqrt{\frac{150}{49}}}$$
Rewrite the square root of the division $\sqrt{\frac{150}{49}}$ as the division of square roots $\frac{\sqrt{150}}{\sqrt{49}}$.
Factor $150=5^{2}\times 6$. Rewrite the square root of the product $\sqrt{5^{2}\times 6}$ as the product of square roots $\sqrt{5^{2}}\sqrt{6}$. Take the square root of $5^{2}$.
