srt of 221
let X = N^1/r (where x= 221^1/2)
therefore
N = (221) and r = 2
from N - R formula
Xn+1 = 1/r{Xn( r- 1) + N/(Xn^[r - 1])}
=1/2{Xn + N/Xn}
the series of squaes of numbers from 10 are
100,121,144,169,196,225
since 221 lies betwen 196 and 225 then its sqrt lies between 14 and 15.so we can take Xo = 14
when X = 0 when X = 1
X1 = 1/2{14 + 221/14} X2 = 1/2{14.893 + 221/14.893}
X1 = 14.893 X2 = 14.866
Therefore the square rot of 221 = 14,866 {correct to 3dps}