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How to Get the Square Root From a Natural Number

A natural number is any positive integer. Zero is sometimes included in the set of natural numbers, but not everyone agrees that it belongs in the set. The square root of any natural number is a mathematical function that yields a value smaller than the natural number. When multiplied by itself, this value converts back to the natural number. The square root function can be applied using the Babylonian method. This method requires you to engage in a process of averaging and estimating, and works for a natural number of any magnitude.

Instructions

    • 1

      Represent the natural number with P.

    • 2

      Choose another number smaller than P and represent this number with Z. For example, if P = 6, then choose Z = 3 or Z = 2.

    • 3

      Find the average of Z and P/Z, and represent this result with A. The average A = [Z + (P/Z)]/2. For example, if P = 6, and Z = 3, then the average A = [Z + (P/Z)]/2 = [3 + (6/3)]/2 = 5/2 = 2.5.

    • 4

      Use the value of A calculated in step 3 as a replacement for the value of Z. For example, if P = 6 and Z = 3 so that A = 2.5, then the new value for Z = 2.5.

    • 5

      Repeat steps 3 and 4 until Z and (P/Z) are approximately the same value. For example, if Z = 2.5, it follows that (P/Z) = (6/2.5) = 2.4. The difference between 2.5 and 2.4 is 0.1. Steps 3 and 4 are repeated until this difference is equal to or close to zero.

    • 6

      Set the square root of the natural number P to be Z when Z = P/Z. For example, when P = 6, the final value for Z = 2.45 = P/Z = (6/2.45).

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