Square Root Calculator
Calculate the square root of any non-negative number. Shows exact value for perfect squares and full decimal precision for irrational roots. Includes the Babylonian (Newton's method) estimation steps for learning.
Enter a non-negative number and press Calculate. The calculator returns: - Exact value (e.g., √25 = 5) - Decimal approximation to many decimal places for irrational roots - Whether the number is a perfect square - Verification: result² = original number
Examples: - √144 = 12 (perfect square) - √2 ≈ 1.41421356 (irrational)
√x = y where y² = x (and y ≥ 0)
Perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 give whole-number square roots.
The square root of a negative number is not a real number (it is imaginary: √-1 = i).
Estimation (Babylonian method): Start with a guess g. Improve by g₁ = (g + x/g) / 2. Repeat until convergence.
Irrational square roots: √2, √3, √5 etc. are irrational — their decimal expansion never terminates or repeats.
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