So, the way you would go about doing square root extraction is by using an analog multipler. An analog multiplier has three inputs Vx, Vy & Vz. The output is given by Vo = (Vx*Vy)/Vz; If we set Vy = 1V and Vo = Vz through a feedback loop, we get Vo.^2 = Vx => Vo = sqrt(Vx).

If the interviewer further asks about an analog multiplier, you could mention that it can be designed by a combination of logarithmic/anti-logarithmic amplifier and an adder.