Help me with the Babylonian method to find the square root of 80? Will fan and medal!

Question

welshfella · Answer

wow - never heard of it

anonymous · Answer

aww, it's ok.

anonymous · Answer

th babylonian method involves two step:
1. make a guess
2. put your guess in babylonian method (BM) equation

i'll give an example
suppose you have to find square root of 27
step 1:-we know that square root of 25 is 5
           so square root of 27 should be around 5.2(just a guess)
step 2:- putting our guess (5.2) in BM equation
         $$\frac{ r+x/r }{ 2 }$$

       here r is our guess=5.2
        x is the value we want to calculate the square root of = 27

     solving it i get 5.196(which is closer to my guess)


try it with your number
:)

p0sitr0n · Answer

Basically what you try to do is smartly guess a number, such that whenever you square it + $$\epsilon$$ error, you get close to your number. Then you shift values and repeat

anonymous · Answer

Thanks guys! :)

welshfella · Answer

interesting..

anonymous · Answer

now if you want to increase the accuracy of your answer, put back the value you got in BM equation

welshfella · Answer

so for square root of 80, as square root of 81 = 9,  8.9 would be a good guess  (I guess!)

anonymous · Answer

yes ! ..even if your guess is way off the actual value, it ultimately gets closer to the actual value as you increase the accuracy

anonymous · Answer

Thanks! I got the questions right @nitishdua31

anonymous · Answer

no problem :)