We also calculated the root by three different methods which give the same result. It is interesting that just after 4 iterations, the Newton’s method finds 16 correct significant digits which is the limit precision for most computers. We can also use Calcpad to create a tiny program for that: We will use the same approach, as follows: Now, lets use it to calculate √a = ?, for a = 5. If we substitute the above equations into the Newton’s iterative formula, we get: In the above formulas, f( x) is the function and f′( x) is the first derivative. Stop when you reach the desired precision.Continue the iterations by using the previous result to estimate a new one:.Calculate the next approximation of the root by the equation: x 1 = x 0 − f( x 0)/ f′( x 0).It is good to be close to the solution, so you can use the nearest exact root. This is an equation of type f( x) = 0 and we can solve numerically it using the Newton’s method: Square rootīy squaring both sides and moving a to the left side, we obtain the following equation: It is so easy and elegant, so I will share it here for the sake of the good old math science. Our brains become lazy and we are losing some knowledge and skills. However, being almost irreplaceable, computers makes us more and more adjective. Sometimes, when we see the ancient marvels of engineering, we wonder: “How they designed this without computers”? And the answer is: “with knowledge, inspiration and hard work”. Today, technologies make everything easy and fast for us.

Calcpad not equal sign