Find Square Root Of Given Number - Python

Given an integer X, find its square root. If X is not a perfect square, then return floor(√x). For example, if X = 11, the output should be 3, as it is the largest integer less than or equal to the square root of 11.

Using built-in functions

We can also find the floor of the square root using Python’s built-in exponentiation operator (**) and then integer conversion.

3

Explanation: x**0.5 calculates the square root of x, and int(sqrt) converts it to the largest integer less than or equal to the sqrt.

Using numpy + math library

The same result can be obtained by using the numpy.sqrt() function to compute the square root and then applying math.floor() to round it down to the nearest integer.

3

Explanation:np.sqrt(10) function computes the square root of 10, resulting in approximately 3.162. The math.floor(sr) function then rounds it down to 3

Note: numpy.sqrt() returns a Numpy array if the input is an array, and a single value if the input is a single number.

Using Binary search

We can also use binary search to do the same task, making it more efficient than brute-force approaches. Instead of iterating through all numbers, it repeatedly halves the search space, significantly reducing the number of calculations.

3

Explanation: If x is 0 or 1, it returns x. Otherwise, it initializes start = 1 and end = x // 2 and performs binary search. It calculates mid and checks if mid² == x. If not, it adjusts start or end accordingly, storing the closest possible square root (ans).

Using Brute force

To find the floor of the square root, try with all-natural numbers starting from 1. Continue incrementing the number until the square of that number is greater than the given number.

4

Explanation: Increment i while i * i is ≤ x. Once i * i exceeds x, it returns i - 1 as the largest integer whose square is ≤ x.