Let y=√x⋯(i)
Where x=36 & Δx=0.6
Now, we know
Δy=√x+Δx−√x
⇒Δy=√36.6−√36
⇒Δy+6=√36.6⋯(ii)
We know that Δy=(dydx)Δx
and
dydx=ddx(√x)=12√x
Then
Δy=(12√x)Δx
=0.62×√36
=0.62×6=0.05
From equation (2), we get
Δy+6=√36.6
∴√36.6=6.05
Hence, the approximate value of √36.6 is 6.05.