square root of 221

Question

Steps to find the square root of 221.

Answer 1

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}