"Square Root of 2" : Decimal System vs. Sexagesimal Systems?

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Does the "Square Root of 2" have "Less Significance" in the Decimal System compared to other Number Systems?

Recently, I learned that the Babylonian Civilization has a number system of "base 60" (sexagesimal) compared to "base 10" (decimal):

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I always wondered where the need would have come to specifically calculate the "Square Root of 2" - is this because somehow "square root of 2" naturally comes up a lot more frequently in the sexagesimal system compared to the decimal system? And does anyone why the specific numbers 24, 51, 10 appear in the above formula?

Thanks!