what was developed first , the mthod or the result , of finding square root of a natural number?

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I was wondering , whether the methods for finding square root of a number were developed first and then by using them value of square root of any number was found OR first the value of square root of any number was found manually by hit and trial method and then methods that would give the approximate value of that square root were developed later ? Please clarify my confusion.

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Square root is thousands of years old; people tried calculating its approximate value waaay before the concept of irrational numbers was introduced:

https://en.wikipedia.org/wiki/Square_root#History

Although, actually, irrational numbers are also thousands of years old (dating back to ancient Greece), but square root seems older:

https://en.wikipedia.org/wiki/Irrational_number#History