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javascriptsqrt

How to calculate the square root without using library and built-in methods in Javascript?

Please help me to write a function to compute the square root of positive real numbers using the formula:

x i+1 = (1/2) * (xi + (A / x1)),

where 'A' - input real number.

On the zero iteration next statements have been taken x0 = A The error should be at least 10-6

Output

sqrt (2) = 1.414
sqrt (9) = 3
sqrt (25) = 5
Solution

  • You could take xi (x) and the new value of xi + 1 (x1) and check if the values are equal. Then end the series and return that value.

    For starting, you need an apporopriate value like the half of the given value.

    function sqrt(a) {
    var x,
        x1 = a / 2;
        
    do {
        x = x1;
        x1 = (x + (a / x)) / 2;
    } while (x !== x1);
    return x;
}

console.log(sqrt (2)); // 1.414
console.log(sqrt (9)); // 3
console.log(sqrt (25)); // 5