WebToolArcHow to use this Perfect Square Calculator
Enter a whole number to test it exactly, see its integer square root, and compare the nearest lower and higher perfect squares.
What it calculates
Check whether a non-negative whole number is a perfect square and find the nearest perfect squares.
Browser limits
Exact integer radical factorization is capped at 1 trillion for responsive local processing. The long-division page supports up to 60 integer digits and 12 generated decimal places.
Perfect squares are an integer property
A non-negative integer is a perfect square when its square root is also an integer. Floating-point square-root output alone is not a reliable proof for very large integers because binary floating-point values can round. Integer arithmetic or an exact integer-square-root check is the safer verification method.
Useful checks around the result
If n is reported as a square, multiply the integer root by itself and confirm that it equals n exactly. Negative integers are not perfect squares over the real integers, although complex-number equations use a different domain. For values close to a square, compare the neighboring integer roots rather than rounding an approximate decimal square root and assuming the rounded value proves exact equality.