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Square root algorithm

The process of finding square root of a number can be divided into two steps. One step is to find integer part and second one is for fraction part.

Algorithm

We derive an algorithm for finding square root here −

START

Step 1 → Define value n to find square root of

Step 2 → Define variable i and set it to 1 (For integer part)

Step 3 → Define variable p and set it to 0.00001 (For fraction part)

Step 4 → While i*i is less than n, increment i

Step 5 → Step 4 should produce the integer part so far

Step 6 → While i*i is less than n, add p to i

Step 7 → Now i has the square root value of n

STOP

Pseudocode

The pseudocode of this algorithm can be derived as follows −

procedure square_root( n )

SET precision TO 0.00001

FOR i = 1 TO i*i < n DO

i = i + 1

END FOR

FOR i = i - 1 TO i*i < n DO

i = i + precision

END FOR

DISPLAY i AS square root

end procedure

Implementation

Implementation of this algorithm is given below −

#include <stdio.h>

double squareRoot(double n) {

double i, precision = 0.00001;

for(i = 1; i*i <=n; ++i); //Integer part

for(--i; i*i < n; i += precision); //Fractional part

return i;

}

int main() {

int n = 24;

printf("Square root of %d = %lf", n, squareRoot(n));

return 0;

}

Output

Output of the program should be −

Square root of 24 = 4.898980