Schriftliches Wurzelziehen - OHNE Quadratzahlen!

When I was a student I had no idea this existed. I struggled with square numbers to no avail, but there is actually a method to put down roots in writing for smaller numbers. It works even in my head. Putting down roots in my head without knowing square numbers, why isn't it really important as a student right now that this method only works with square roots. You cannot calculate third, fourth or 17th roots with it and I would like to warn you that the method is a little complicated at first, but once you understand it, it works.

It's actually pretty good and it's even a little funny, so if you can't concentrate right now, you'd better watch the video another time, otherwise you'll just get frustrated and that's not the point. There are different ways to draw roots in writing. I'm all for one where you don't really have to be able to do square numbers, but the calculation takes more space and To help you understand why all this can work, I want to show you a really surprising little thing: if you add odd whole numbers one after the other, you will always get a square number.

The prerequisite for this is that, on the one hand you only take positive numbers and on the other hand you start with one 1 + 3 = 4 4 is a square number because 2 h 2 makes 4 the 2 as a base shows how many odd numbers you have added another example 1 + 3 + 5 is 9, we have added three numbers and 3 h 2 makes 9, we count 7 consecutive odd numbers together which should give 49 because 7 x 7 49 1 + 3 + 5 + 7 + 9 + 11 + 13 in reality ago 49 and you pay They are too, so now you can continue, but it is not necessary because it is only important to know if you want to understand why written root extraction works and to be able to introduce you to the method. now I have to rotate the image because you need some space at the bottom the higher the number the more space you will need.

We'll start right away with a nice long number so that a certain routine works right away. 1867141 we want to take the root of that immediately let's start from the back we have to divide the number below the root into two blocks and start from the right. Here it may happen that the first two blocks only consist of one number, but that doesn't matter and now we start again from the beginning and that means we calculate downwards because it is on the right. In the end, it's really just the result. We start by subtracting odd numbers one after another from the first block of two, ie. of 18, and we start with 1 -1 -3-5 - 7.

Now we have to stop because we can only subtract until a zero appears in the result or the next positive number 18- 1 - 3- 5- 7 make 2 we write these 2 as a result of subtraction and now comes the clue, now we count how many numbers we have subtracted and this number is the first digit of the actual result vi is the first digit of the root, then we take the next block of two and we take it down and we write after the result of the last subtraction. The number we are now subtracting is 267 and then we drag the 1 back, and so on, that takes forever, no we don't.

Let's do that because in the result we recite digit by digit so when subtracting a maximum of nine numbers can be subtracted that's why as soon as we know part of the result we have to multiply it by two that have four. We just discovered it, so we multiply it by 2 and we get 8. Now we write this 8 below the 267 so that a place is free, which we add with a 1. The number we subtract is now 81 and now we put the row back -83 -85 and more is not possible because the intermediate result is now 18 and we can no longer subtract the 87 from it - it would result in a negative number and that should not happen here.

Now we count again how many subtractions we have done, which were three, the three enter the result and now we know the first two digits of the root, the next block of two is the turn, we write the 10 after the 18 and now we have to subtract of 1810 but first we have to add what we have so far. We multiply the result by 2, 43 is in our result multiplied by 2, which gives 86. We write it again under 1810 so that there is a free position and we replace it with 1, a minus in front of the whole number and we can subtract again -861 and - 863 then it's over again because there are 86 left, these were two numbers that we subtracted, the Z enters the result, the last two blocks are the following, we lower the 41 and multiply the 432 of the result by 2, that's 864 the digit is complemented by a 1 and a minus comes in front of the number and here it actually comes out zero so we're done, well we've almost subtracted once so the one still has to be included in the result but now we are done 4321 is the root of 1867141 and because even with the best explanation you can quickly no longer understand something or misinterpret something, there is another example this time with a decimal number because you also have to know when the comma appears in the result, now we want the root of 2, 25 Knowledge again we divide the number from right to left into groups of two.

The comma here has no importance for us. 25 belongs to a group of two and in this example the first group of two only consists of one number, so here we go, we remove the 1 from there the Z comes out and it is no longer possible, we have subtracted a number, so we write 1 in the result. We go down the next group of two and now we have to continue calculating with 125. Since we are already past the decimal point, we have to put it in that too. We write the result of the result, multiply it by 2 again. and we write it as a tens below 125, one after and a minus in front and we have the initial number with which we continue the calculation -2 -23 -25 and so we continue happily until 0 because this example is already over.

We have subtracted five numbers, so we write the five and the result is the root of 2.25, so 1.5 you can still get along, but I hope that there is a comma in the result and not too much below the root. so you also have to know here when the decimal point comes in. Let's calculate the root of Z. We can't divide anything here. There is only one number of the two. We can also simply subtract the one and get the first partial. result but now we have to somehow get a block down from two because there is no zero as a result of the subtraction.

Stupidly, there are no more numbers at the top. In such a case, you type two zeros and as soon as you do that, a comma should appear in the result. Of course, only the first time you add two zeros again, then you don't write another one, the result appears, there are no numbers like that, and then you continue calculating normally. , the result is multiplied by two, followed by a one and then you become cheerful, subtract the number of subtractions from the result and so on. The special feature is that you still have to add a block of two in each step.

You have to keep adding two zeros, even if the number under the root is already over, but that's really it. The only special feature is that the calculation itself is the same, but the root of 2we is long and we stop in three places. after the decimal point, which would otherwise be out of scope. At the bottom, we are left with 604, to which we could add zeros again and, of course, continue with the calculations. Is the root of 2 1.414 in any case if it stops after three? places after the decimal point, the longer the number is below the root, the longer your calculation will be, of course.

You should definitely pay attention to clarity because if you can no longer see it for yourself, there is a good chance you will miscalculate. , it is advisable to perform the subtractions in a secondary calculation step by step so that the actual calculation of the task is clear. Then it won't be a problem if you make a mistake in the secondary calculation. You can then recalculate it and write it down and The actual root extraction is still clear, this method needs a little practice, especially with numbers of different lengths and a variety of results, but once you master it, the only difficulty is performing Keep track of things and not make a miscalculation. when doing subtractions You have just learned a practical method for extracting square roots