An experiment from `X = (a^(1//2) b^(2))/( c^(3))` . If the percentage errors in ` a, b , and c are +- 1% , +- 3% , and +- 2%` , respectively , then the percentage error in `X` can be

Options

A. `+- 12.5%`
B. `+-7%`
C. `+-1%`
D. `+-4%`

Answer

A

Explanation

` X = ( a^(1//2) b^(2))/(c ^(3))`
`( Delta X)/( X) xx 100 = (1)/(2) ( Delta a)/( a) xx 100 + 2 ( Delta b)/( b) xx 100 + 3 ( Delta c )/( c ) xx 100`
` = (1)/(2) xx 1 + 2 xx 3 + 3 xx 2 = 12.5%`