Using the concept of differentials, √36.6 is approximately equal to:

The correct answer is Option (1) → 6.05

Let $f(x)=\sqrt{x}$

$f(36)=\sqrt{36}=6$

$Δx=0.6$

so $f(36+0.6)=f(36)+\frac{dy}{dx}Δx$

$=6+\left(\frac{1}{2\sqrt{x}}\right)×0.6$   $[x=36]$

$=6+\frac{1}{12}×0.6=6.05$