Square Root Calculator
Square root plus perfect-square detection and precision digits.
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About this calculator
Square roots invert squaring. Perfect squares (1,4,9,…,169,196…) have integer roots — useful mental-maths anchors between them.
Formula
√x · Newton's method converges quadratically: xₙ₊₁ = (xₙ + N/xₙ)/2.
Frequently Asked Questions
Estimate √200 without a calculator?
Between 14 (196) and 15 (225); 196 is close so ≈14.14 — actual 14.142.
Why do negative numbers fail here?
No real number squared gives a negative; those roots live among imaginary numbers (√−9 = 3i).