Solution:

Let \( Y = (PQ)^{1/2} \). Its value is \( Y = (1 \times 4)^{1/2} = 2 \, \text{m} \). The relative error is \( \frac{\Delta Y}{Y} = \frac{1}{2} \left(\frac{\Delta P}{P} + \frac{\Delta Q}{Q}\right) = \frac{1}{2}\left(\frac{0.40}{1} + \frac{0.20}{4}\right) = 0.225 \), giving \( \Delta Y = 0.45 \, \text{m} \). Thus, \( Y = (2 \pm 0.45) \, \text{m} \).