Rewrite the square root of the division $\sqrt{\frac{2176}{2401}}$ as the division of square roots $\frac{\sqrt{2176}}{\sqrt{2401}}$.
$$\frac{\sqrt{2176}}{\sqrt{2401}}$$
Factor $2176=8^{2}\times 34$. Rewrite the square root of the product $\sqrt{8^{2}\times 34}$ as the product of square roots $\sqrt{8^{2}}\sqrt{34}$. Take the square root of $8^{2}$.