Untitled

def sqrt_approximation(x: float):
    # This function calculates an approximation of the square root of the input x
    # using the formula (x + 17/x) * 0.5, where 0.5 is the initial guess.
    
    approximation = 0.5
    formula_result = (x + 17 / x)

    return approximation * formula_result


result1 = sqrt_approximation(20)
result2 = sqrt_approximation(result1)
result3 = sqrt_approximation(result2)
result4 = sqrt_approximation(result3)

print(f"{float(result1):.3f}")
print(f"{float(result2):.4f}")
print(f"{float(result3):.6f}")
print(f"{float(result4):.8f}")