Good afternoon, dear guests and subscribers of my channel!
Remember when we were taught in school to extract square roots without a calculator? Rather, this operation has long been forgotten because it is complex. Despite the fact that such calculations are very rarely applicable in everyday life, there is a method that can hardly be forgotten by calculating any square root with it at least once.
The only thing you need to remember is the table of squares of numbers, which is studied in high school, like the multiplication table in primary:
Usually, to extract the square root without electronic computing devices, we are forced to produce selection of a number, performing the opposite operation - by squaring it and so on until " let's miss "!
So the original way is:
Let's say we need to calculate the square root of 200.
Looking at the table of squares, it can be understood that the number 200 is between 196 (14 ^ 2) and 225 (15 ^ 2). Therefore, the root of 200 can be represented as the sum of 14 and a fraction, denoted by X. Then, our expression will take the following form:
Now, square both sides of the equality and expand the brackets on the right side:
Due to the fact that X ^ 2 is a very small value, we neglect it, then we get:
We calculate X and it will be equal to 1/7, substitute X into the equality and get:
This result was obtained with an accuracy of 0.1 and certainly it is rounded, since we threw X ^ 2 and usually, in life, without making complex and accurate calculations, this value is enough. But, if you need to calculate the value when extracting the square root with an accuracy of 0.01, then the operation can be repeated and the newly obtained expression is already squared by entering Y into the turn:
Here we also discard Y ^ 2 and find the value of Y, after which we even more accurately calculate the desired square root of 200:
Further, we operate with this resulting number, or reduce to a common denominator and calculate.
Having calculated the value, we get 14.14, which corresponds to the correct value, rounded to the nearest hundredth:
If it is required even more precisely, then the operation is repeated, and each time, performing the same actions, we increase the accuracy of the calculation.
The method is worthy and deserves attention!
I hope you enjoyed the article and became useful!
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