Question

Using differentials, find the approximate values of:

find the approximate values of √37.

Answer 1

Let y = √x.

Let x = 36 and Δx = 1.

As y = √x.

∴ Δy = 0.08

Also,

Δy = f(x+Δx) - f(x)

∴ 0.08 = \(\sqrt{36+1}\) - √36

⇒ 0.08 = √37 – 6

⇒ √37 = 6.08