Using differentials, find the approximate value of each of the following up to 3 places of decimal.

Consider y = √x.

Let x = 49 and Δx = 0.5. Then, we get

Δy =

= √49.5-√49

= √49.5 – 7

= √49.5 = Δy + 7

Now, dy is approximately equal to Δy and is given by:

dy =

= 0.035

Therefore, the approximate value of is 7.035.