**Solution:** To find the degree, remove the fractional exponent by squaring both sides: $\left[\,1 + \left(\dfrac{dy}{dx}\right)^2\right]^3 = \left(\dfrac{d^2y}{dx^2}\right)^2$ Now the equation is polynomial in derivatives, and the highest order derivative is $\dfrac{d^2y}{dx^2}$ appearing as a square term. Therefore, **Degree = 2** $\boxed{\text{Answer: (D) 2}}$