The Sqrt(x) algorithm is a very interesting question that you may have heard in your school or college asked in many interviews including FAANG companies.

The question for an algorithm is,

Given a non-negative integer x, return the square root of x rounded down to the nearest integer. The returned integer should be non-negative as well.

You must not use any built-in exponent function or operator.

For example, do not use pow(x, 0.5) in c++ or x ** 0.5 in python.

Example 1:

Input: x = 4

Output: 2

Explanation: The square root of 4 is 2, so we return 2.

Example 2:

Input: x = 8

Output: 2

Explanation: The square root of 8 is 2.82842..., and since we round it down to the nearest integer, 2 is returned.

Let's start with the algorithm,

var mySqrt = function(x) {

    let r = x

    while (r * r > x) 


        r = ((r + x / r) / 2) | 0;


    return r;


Here is just a formula used where we are running a loop until (r*r > x). Inside the loop, we have been calculating the value of r = ((r + x / r) / 2). When the loop end we just return the value of r.

I hope you understood the algorithm. If you have any doubts, please let us know in the comments.