math

How to find the Nearest Square Root Without Using Calculator using Babylonian Method

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\/645 = ..

1. find any complete square root that very close to 645

25^2 = 625
26^2 = 676

–> 626 < 645 < 676

a = 25
so we use 25 because 25^2 is the nearest to 645

2. next step is –> 645/a

645/25=25.8

b = 25.8

3. next –> (a+b)/2 = c

(25+25.8)/2 =~ 25.39

c =~ 25.39

25.39^2 = 644.6521
25.40^2 = 645.16

25.39^2 < 645 < 25.4^2

\/645 ~= 25.39

if we use calculator, square root of 645 is

\/645 = 25.396850198400588274475113495221

not bad, right? :