Square Root Calculator

Number

Accepts integers or decimals. Negative values return the principal complex root (i·√|x|).

Precision (decimal places)

Controls the displayed result only; internal math uses PHP sqrt().

Drag & drop a text file with a single number (or click to choose). Nothing is uploaded; parsing happens in your browser.

Square Root – Quick Cheat Sheet

Definition: √x is the non-negative number whose square is x (real domain x ≥ 0).
Perfect squares: If x = n² (n integer), then √x = n exactly.
Decimals: Results may be irrational (non-terminating). We show a rounded approximation.
Negative inputs: √x is not real. Principal complex root is i·√|x|.
Simplest radical form: For integer x, √x can be written as a√b with b square-free (e.g., √98 = 7√2).
Precision: Only affects display rounding; internal computation uses floating-point sqrt.

Tips & edge cases

Very large integers may skip radical simplification to keep the page fast (tries up to 1e12).
Rational inputs like 0.25 have exact roots (√0.25 = 0.5); others like √2 are irrational.
“Squared back” is a quick sanity check (may differ slightly due to rounding).