If percentage error in a, b, c, d are 1% 2% 3% and 4% respectively. What will be the percentage error in `X= (a^(1//3)b^4)/(cd^(2//3))`

Answer

`+-14%`

Explanation

Here, `X = (a^(1//3)b^4)/(cd^(2//3))`
Max. percentage error in X is given by
`(DeltaXxx100)/(X) = +-[(1)/(3)(Deltaa)/(a) +4(Deltab)/(b) +(Deltac)/(c ) +(2)/(3) +(Deltad)/(d)]`
`=+-[(1)/(3)xx1% +4xx2% +3% +(2)/(3)xx4%]`
`=+-[(1)/(3) +8 +3 +(8)/(3)]% = +-14%`