A number is square root of if

Most programming languages have an in-built sqrt function. But it can be easily calculated using binary search.

float sqrt(n) {
    low = 0.0;
    high = (float)n+1;
    while ((high-low) > 0.00001) {
        mid = (low+high) / 2;
        if (mid*mid < n) {
            low = mid;
        }
        else {
            high = mid;
        }
    }
    return low;
}

Note that we do not check high - low == some_value This is because we never equate float values. Instead, we use a small epsilon value and use that as an error tolerance.

Newton Raphson Method:

#include <stdio.h>
// Function to get absolute value of the number given by user.
float absolute(float num)
{
    if(num < 0){
        num = -num;
    }
    return num;
}
// Function to calculate square root of the number using Newton-Raphson method
float square_root(int x)
{
    const float difference = 0.00001;
    float guess = 1.0;
    while(absolute(guess * guess - x) >= difference){
        guess = (x/guess + guess)/2.0;
    }
    return guess;
}

int main()
{
    int number;
    float root;
    printf("Enter a number: ");
    scanf("%i", &number);
    root = square_root(number);
    printf("The square root of %i is: %f", number, root);
    return 0;
}

Float values can be rounded to their floor values and ceil values. This is not rounding as rounding happens to the nearest integer, while in floor and ceil we specify which nearest integer we are rounding to.

Most programming languages have in-built floor and ceil functions.

floor(5.9) = 5
ceil(1.1) = 2
floor(-1.1) = -2
ceil(-2.1) = -2

C ++ Implementation :

#include <iostream>
#include <cmath> // library support is needed
using namespace std ;
int main(){
    cout << floor(5.9) << endl ;
    cout << ceil(1.1) << endl ;
    cout << floor(-1.1) << endl ;
    cout << ceil(-2.1) << endl ;
    return 0 ; 
}

Python Implementation :

import math # libraray support is needed
print int(math.floor(5.9))
print int(math.ceil(1.1))
print int(math.floor(-1.1))
print int(math.ceil(-2.1))