Question

Two measured quantities are given as A= 1.0m ± 0.2m and B = 2.0m ± 0.2m. what is the reported correct value of
$({ab})^{ \frac{1}{2} }$
​

Answer 1

Solution:

$let \: z = ({ab})^{ \frac{1}{2} } ......(i)$

∆Z/Z =½ ∆A/A +½ ∆B/B......(ii)

$z = ({2.0})^{ \frac{1}{2} } = 1.414$

∆Z=$\frac{1}{2} ( \frac{0.2}{1.0} + \frac{0.2}{2.0} ) \times 1.414 = 0.21$

As A and B both are having two significant figures so reported correct value of (AB)^½ is 1.4m ± 0.2m.

Hope this will help you ❤

Answer 2

∆Z=

$\frac{1}{2} ( \frac{0.2}{1.0} + \frac{0.2}{2.0} ) \times 1.414 = 0.21$