Solution:
Using error propagation: \(\frac{\Delta Z}{Z} = \frac{1}{3}\frac{\Delta A}{A} + 2\frac{\Delta B}{B} + \frac{1}{2}\frac{\Delta C}{C}\). Substituting values: \(\frac{1}{3}(0.3) + 2(0.2) + \frac{1}{2}(0.6) = 0.1 + 0.4 + 0.3 = 0.8\).
In an experiment \(Z\) is measured as \(Z = \frac{A^{1/3} B^2}{\sqrt{C}}\). Relative error in given quantities \(A\), \(B\), & \(C\) are 0.3, 0.2 & 0.6 respectively. Find maximum relative error in \(Z\).
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