In modern times, calculators, laptops or smartphones, are the ones that are taking care of even the simplest tasks, in this sense, there are thousands of calculations that we do through our calculators, even for sums or subtraction of simple numbers that were taught to us in our first years in a school.
In this article, we take care of telling you how to calculate or rather how to do the square root of 2, a number that does not have an exact number as its root, but rather a decimal number, get ready, take a pencil and a notebook and discover this way, simple and fast, which will help you later to calculate any square root without the need for a calculator.
The square roots are usually a nightmare when we are in school, and in the case of some already grown up too. These days, as we mentioned before, many schools are giving up teaching it, because it seems obsolete, since it is an operation that can be optimized through the correct use of a calculator.
These methods that we talk about in this article, not only allow us to be able to solve square roots quickly and correctly, but also provide us with a verification mechanism for our results.
What do you need for how to do the square root of 2?
- Pencil
- Notebook
Trial and error method
- Trial, iteration, or guessing consists of selecting an approximation to what we consider to be a logical result. That is to say that we start from this approximation, to this initial number in this case (we are thinking of a number that turns out to be the square root of 2) we must calculate what its square is.
- Then we proceed to make a comparison between the number that we approximate with the number squared, in this case 2. Depending on the result of our error, we proceed to change our number, getting closer and closer to the final result.
Trial Method Recommendations
This method is simple, but it is not very pedagogical, when you want to teach what is the objective of square roots, much less what is the concept of this mathematical tool, so it is recommended to be introduced in an advanced mathematics course in school, or it can also work if it is taught or taught as an alternative method of checking results, compared to those obtained through the calculator.
Algorithm that allows you to solve any square root without the need for any calculator
Although the trial and error method is simple, it is also a method that requires work, patience, and can even get a bit tedious. For this reason, we also proposed this algorithm, with which we guarantee you will not have to calculate any other square root with your calculator.
- You must estimate the first digit of the square root you want to obtain. In this sense you have to think about the exact square roots and compare them with the number you are calculating. In our case, we are working with 2 so the square roots that are close are the square root of four and the square root of 1, so our value must be between these two numbers.
- The second step consists of dividing this first number by the number of the square root that you want. In our case, our data is two: 1, which is the first number, and 2, which is the number we are looking for the root of.
- Once we conclude the previous step, we look for the average between the quotient and the denominator, in this way we find the new approximation. You estimate the error and that’s it.