{"id":653,"date":"2024-10-10T13:39:46","date_gmt":"2024-10-10T08:09:46","guid":{"rendered":"https:\/\/codexplained.in\/?p=653"},"modified":"2025-11-24T15:58:33","modified_gmt":"2025-11-24T10:28:33","slug":"find-square-root-without-using-sqrt","status":"publish","type":"post","link":"https:\/\/codexplained.in\/?p=653","title":{"rendered":"Find Square Root (without using sqrt)."},"content":{"rendered":"
\n#include <stdio.h>\n\ndouble squareRoot(double N) {\n    if (N < 0) {\n        printf("Negative numbers do not have real square roots.\\n");\n        return -1; \/\/ Indicate an error for negative input\n    }\n\n    double guess = N; \/\/ Start with the number itself as the initial guess\n    double epsilon = 0.00001; \/\/ Define the accuracy level\n    double newGuess;\n\n    \/\/ Repeat until the guess is close enough to the actual square root\n    do {\n        newGuess = (guess + N \/ guess) \/ 2; \/\/ Update guess using the formula\n        \/\/ Check if the difference is within the acceptable range\n        if (newGuess - guess < epsilon && newGuess - guess > -epsilon) {\n            break; \/\/ If close enough, break the loop\n        }\n        guess = newGuess; \/\/ Update the guess\n    } while (1);\n\n    return newGuess; \/\/ Return the approximated square root\n}\n\nint main() {\n    double number;\n\n    printf("Enter a number to find its square root: ");\n    scanf("%lf", &number); \/\/ Take user input\n\n    double result = squareRoot(number); \/\/ Call the function\n    if (result != -1) { \/\/ Check for negative input\n        printf("The square root of %.2lf is approximately %.5lf\\n", number, result);\n    }\n\n    return 0;\n}\n\n<\/pre><\/div>\n\n\n
Explanation:<\/h2>\n\n\n\n
The program uses the Newton-Raphson method<\/strong>, an iterative technique to estimate the square root of a number.<\/p>\n\n\n\n
Key Components<\/h3>\n\n\n\n
    \n
  1. Function squareRoot(double x)<\/code><\/strong>:\n
      \n
    • Starts with an initial guess (g = x \/ 2<\/code>).<\/li>\n\n\n\n
    • Iteratively improves the guess using the formula: g=g+xg2g = \\frac{g + \\frac{x}{g}}{2}g=2g+gx\u200b\u200b<\/li>\n\n\n\n
    • Continues until the guess is sufficiently close to the actual square root (within a small threshold, epsilon<\/code>).<\/li>\n<\/ul>\n<\/li>\n\n\n\n
    • Main Function<\/strong>:\n
        \n
      • Prompts the user for a number.<\/li>\n\n\n\n
      • Checks if the number is negative (since square roots of negatives are not real).<\/li>\n\n\n\n
      • Calls the squareRoot<\/code> function and displays the result<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n
        Output:<\/h2>\n\n\n\n
        1.Enter a number to find its square root: -9 \nCannot compute square root of a negative number.\n\n2. Enter a number to find its square root: 36\nThe square root of 36.00 is approximately 6.00000\n\n3. Enter a number to find its square root: 50 \nThe square root of 50.00 is approximately 7.07107<\/code><\/pre>\n