Question : The sulbasutras of ancient Indian Scholar “Baudhayan” have reached to a most correct value of which among the following?

Answer :
√2
Notes:
The sulbasutras of ancient Indian Scholar “Baudhayan” have reached to a most correct value √2. Sulbasutras of Baudhayan contain the geometric solutions and NOT the algebric ones as far as the linear equations are concerned. There are several values of π in Sulbasutras of Baudhayan. There are several values of π derived in Baudhayan’s sulbasutras such as 3.004, 3.114, 3.202, out of which none is particularly accurate. But as fast as values of √2 are concerned, Baudhayan is excellent. The meaning of the Sanskrit shloka in which he talks about the √2 translates as follows:
√2= 1+1/3+1/(3×4)-1/3(3x4x34)=577/408
The value is 1.41421568627451
The value of √2= 1.414213562373095
We see that the value of √2 given by Baudhayan is correct up to 5 decimal places. He it makes an interesting thing to know as even the half of the above translation as √2= 1+1/3+1/(3×4) would have given a value of 1.416, which is correct up to 2 decimal points. The real knowledge of baudhayan reflects in the later part of the shloka where he reduced the 1/3(3x4x34) from this and reaches at a real correct value.