JavaScript Program to Find the Square Root (original) (raw)

Last Updated : 03 Jun, 2024

Given a number N, the task is to calculate the square root of a given number using JavaScript. There are the approaches to calculate the square root of the given number, these are:

Approaches to Find the Square Root of Given Number in JavaScript:

Table of Content

Using Math.sqrt() Method
Using JavaScript Math.pow() Method
Using Binary Search
Newton's Method

**Basic Examples:

Input: num = 25
Output: 2
Explanation: The square root of 25 is 5.
Input: num = -120
Output: NaN
Explanation: The square root of Negative numbers is NaN.
Input: num = 'Geeks'
Output: NaN
Explanation: The square root of String Value is NaN.

Using Math.sqrt() Method

The Math.sqrt() method is used to find the Square Root of a given number.

**Syntax:

Math.sqrt( value )

**Example: In this example we will find the square root using JavaScript Math.sqrt() method.

JavaScript `

const num1 = 25; const num2 = -120; const num3 = 'Geeks';

// Math.sqrt() function returns the // square root of number console.log('Square Root of ' + num1 + ' is ' + Math.sqrt(num1));

// Math.sqrt() function returns NaN, because // the passed value is negative integer console.log('Square Root of ' + num2 + ' is ' + Math.sqrt(num2));

// Math.sqrt() function returns NaN, because // the passed value is string console.log('Square Root of ' + num3 + ' is ' + Math.sqrt(num3));

Output

Square Root of 25 is 5 Square Root of -120 is NaN Square Root of Geeks is NaN

Using JavaScript Math.pow() Method

The Math.pow() method is used calculate the power a number i.e., the value of the number raised to some exponent. To get the square root of any Number, we set the power to 1/2 of that number.

**Syntax:

Math.pow( num, 1/2 )

**Example: In this example, we will calculate the square root of given values using Math.pow() method.

JavaScript `

const num1 = 25; const num2 = -120; const num3 = 'Geeks';

// Math.pow() function returns the // square root of number console.log('Square Root of ' + num1 + ' is ' + Math.pow(num1, 1/2));

// Math.pow() function returns NaN, because // the passed value is negative integer console.log('Square Root of ' + num2 + ' is ' + Math.pow(num2, 1/2));

// Math.pow() function returns NaN, because // the passed value is string console.log('Square Root of ' + num3 + ' is ' + Math.pow(num3, 1/2));

Output

Square Root of 25 is 5 Square Root of -120 is NaN Square Root of Geeks is NaN

Using Binary Search

The binary search is used to find the square root of the given number N with precision upto 5 decimal places.

The square root of number N lies in range 0 ? squareRoot ? N. Initialize start = 0 and end = number.
Compare the square of the mid integer with the given number. If it is equal to the number, then we found our integral part, else look for the same in the left or right side of mid depending upon the condition.
After finding an integral part, we will find the fractional part.
Initialize the increment variable by 0.1 and iteratively calculate the fractional part upto **5 decimal places.
For each iteration, change increment to **1/10th of its previous value.
Finally, return the answer computed.

**Example: In this article, we will calculate the square root of the given Number using Binary Search.

JavaScript `

// Function to find the square-root of N function findSqrt(number) { let start = 0, end = number, mid, ans;

// To find integral part of square
// root of number
while (start <= end) {

    // Find mid
    mid = Math.floor((start + end) / 2);

    // If number is perfect square
    // then break
    if (mid * mid == number) {
        ans = mid;
        break;
    }

    // Increment start if integral
    // part lies on right side
    // of the mid
    if (mid * mid < number) {

        // First start value should be
        // added to answer
        ans = start;

        // Then start should be changed
        start = mid + 1;
    }

    // Decrement end if integral part
    // lies on the left side of the mid
    else {
        end = mid - 1;
    }
}

// To find the fractional part
// of square root upto 5 decimal
let increment = 0.1;

for (let i = 0; i < 5; i++) {
    while (ans * ans <= number) {
        ans += increment;
    }

    // Loop terminates,
    // when ans * ans > number
    ans = ans - increment;
    increment = increment / 10;
}
return ans;

}

// Driver Code const n = 36;

console.log(findSqrt(n));

Newton's Method

Newton's method, also known as the Newton-Raphson method, is an iterative method for finding the roots of a real-valued function. To find the square root of a number using Newton's method:

Start with an initial guess ?0__x_0 for the square root.
Iterate using the formula ??+1=1/2(??+??????/??)until the result converges to the desired accuracy.

Here's how we can implement Newton's method to find the square root of a given number in JavaScript:

JavaScript `

function findSquareRootUsingNewton(number) { if (number < 0) return NaN; // Square root of negative numbers is NaN

let guess = number / 2; // Initial guess

// Iterate until the guess converges
while (Math.abs(guess * guess - number) > Number.EPSILON) {
    guess = (guess + number / guess) / 2;
}

return guess;

}

// Test Cases console.log("Square root of 25:", findSquareRootUsingNewton(25)); // Output: 5 console.log("Square root of -120:", findSquareRootUsingNewton(-120)); // Output: NaN console.log("Square root of 'Geeks':", findSquareRootUsingNewton('Geeks')); // Output: NaN

Output

Square root of 25: 5 Square root of -120: NaN Square root of 'Geeks': NaN