Find out square root of 4.01 using differential .

Explanation

Let y = f(x) = `sqrtx`
x = 4
and `Deltax = 0.01`
Then `Deltay = sqrt(x + Deltax) - Deltax " " ... (i)`
`(dy)/(dx) = f'(x) = (1)/(2sqrtx)`
`Deltay = ((dy)/(dx))_(x = 4) Delta x`
`implies Deltay = ((1)/(2sqrtx)) Deltax`
`implies Delta y = (1)/(4) xx 0.1 = 0.0025 `
Also `Deltay = sqrt(4.01) -2 " "` [using (i)]
`implies sqrt(4.01) = 2 + .0025`
`implies sqrt(4.01) = 2.0025`