find the nth root of a number in rust

To find the nth root of a number in Rust, we can define a function using the power function and a loop to calculate the nth root iteratively.

Here's an example implementation:


main.rs
fn nth_root(x: f64, n: i32) -> f64 {
    // Calculate the initial guess
    let guess = x / (n as f64);

    let mut prev_guess = guess;
    let mut new_guess = (1.0 / n as f64) * ((n - 1) as f64 * prev_guess + x / prev_guess.powi(n - 1));

    // Iterate until the guess converges
    while (new_guess - prev_guess).abs() > 1e-10 {
        prev_guess = new_guess;
        new_guess = (1.0 / n as f64) * ((n - 1) as f64 * prev_guess + x / prev_guess.powi(n - 1));
    }

    return new_guess;
}

fn main() {
    let x = 64.0;
    let n = 3;

    let nth_root = nth_root(x, n);
    println!("{}th root of {} = {}", n, x, nth_root);
}
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