isPerfectSquare

An **IsPerfectSquare** function is a computational tool used to determine whether a given integer is a perfect square. A perfect square is an integer that is the square of another integer, meaning it can be expressed as *n²* where *n* is an integer. For example, 16 is a perfect square because it equals 4², while 20 is not a perfect square since no integer squared equals 20.

The function typically takes a non-negative integer as input and returns a boolean value—either *true* or *false*—indicating whether the input is a perfect square. In programming, this function is often implemented using mathematical operations or algorithms to check for perfect squares efficiently.

One common approach involves calculating the integer square root of the input number and then verifying whether squaring this root yields the original number. For instance, if the input is 25, the integer square root is 5, and 5² equals 25, confirming it is a perfect square. If the input is 24, the integer square root is 4, but 4² equals 16, which does not match 24, so the function returns *false*.

Mathematically, a number *x* is a perfect square if there exists an integer *k* such that *k² = x*. Some algorithms also use binary search or floating-point approximations to determine perfect squares, though these methods may introduce precision errors for very large numbers. For example, in languages like Python, the `math.isqrt()` function can be used to compute the integer square root, and the result can be squared to verify the check.

This function is widely used in mathematical computations, cryptography, and algorithmic problem-solving, where verifying perfect squares is necessary for tasks such as primality testing or solving Diophantine equations. Its simplicity and efficiency make it a fundamental operation in both theoretical and applied mathematics.