 Integer square root

For a nonnegative integer $n$, its integer square root is the unique nonnegative integer $r$ satisfying $r^2\le n<(r+1{)}^2$, equivalently $r=\lfloor \sqrt{n}\rfloor$. Testing $r^2=n$ decides whether $n$ is a perfect square using exact integer arithmetic.

The integer square root of a non-negative integer \( n \) is the largest integer \( k \) such that \( k^2 \leq n \). In other words, it is the greatest integer that, when squared, does not exceed \( n \).