The square root of an odd powered integer is not always irrational; it can yield rational results under specific conditions. For instance, the square root of \(4^3\) equals 8, a rational number. The discussion highlights that Excel may inaccurately represent the square roots of large odd powered integers due to its limitations in floating-point precision, specifically adhering to the IEEE 754 standard. This rounding issue can lead to misleading integer outputs when calculating square roots of such numbers.
PREREQUISITESMathematicians, data analysts, software developers, and anyone interested in numerical computations and their accuracy in Excel.
Did you notice that if you write any of those irrational square roots as a continued fraction, they always repeat.e2m2a said:From the research I have done since posting, it says that the square root of any non-square integer is always an irrational number.
What about 1?e2m2a said:Is it always true that the square root of an odd powered integer will always be irrational?