Question

Find the square root of 3.8 correct to two decimal places

Answer 1

We have to find the square root of 3.8 correct to two decimal places.

solution : let x = 3.8

= 4 - 0.2

= 4(1 - 0.2/4)

= 4(1 - 0.1/2)

= 4(1 - 1/20)

now taking square root of x,

x½ = [4(1 - 1/20)]½

= (4)½ [1 - 1/20]½

= 2 [1 - 1/20]½

from binomial expansion, if y = (1 - x)ⁿ, where x << 1

then, y ≈ 1 - nx

in above expression we see, 1 >> 1/20

so, [1 - 1/20]½ ≈ 1 - 1/40 = 39/40 = 0.975

now x½ = 2 × 0.975 = 1.95

Therefore the square root of 3.8 correct to two decimal places is 1.95

[note : if you want to get more accurate value just use expansion of (1 - x)ⁿ = 1 - nx + n(n - 1)/2! x² - n(n - 1)(n - 2)/3! x³ + .... ]