Question

For $z = a ^{2} x ^{3} y ^{\frac{1}{2}}$, 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 $\%$.

Answer 1

$z=a^{2} x^{3} y^{1 / 2} $
$\frac{\Delta z }{ z }=\frac{2 \Delta a }{ a }+\frac{3 \Delta x }{ x }+\frac{1}{2} \frac{\Delta y }{ y }$
$a$ is constant
$\frac{\Delta z }{ z } \times 100=3(4 \%)+\frac{1}{2}(12 \%)=18 \%$