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A mathematical method for calculating square roots using iterative averaging.
The square root of 123 is a non‑integer irrational number approximately 11.0905365, which places it squarely between the square roots of the nearby perfect squares 121 (√121 = 11) and 144 (√144 = 12) ...
; its square root is irrational and is most correctly left in simplest radical form as √123 (or ±11.0905365... as a decimal approximation) because 123’s prime factorization contains no repeated prime ...
The square root of 123, written , is an with principal (positive) value approximately 11.0905365; the equation x² = 123 has two algebraic solutions ±11.0905365, but the convention √123 denotes the pos...
Two reliable hand methods exist to compute square roots: Newton’s method (the iterative averaging formula often called Heron’s method) quickly refines an initial guess and is what calculators use in p...