For z = a 2 x 3 y 1 2 , where ' a ' is a constant. If percentage error in measurement of ' x ' and ' y ' are 4 % and 12 % , respectively, then the percentage error for ' z ' will be _____ % .

Step-by-step solution

Given: z = a 2 x 3 y 1 2 Relative error is given by ∆ z z = 3 × ∆ x x + 1 2 × ∆ y y Now, maximum percentage error in z is ∆ z z × 100 = 3 4 + 1 2 2 × 100 = 18 % .