I DID IT! Maybe some of you already know this number-power-to-something that ends in 5

Hello,

William here.

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I have figured out a trick that makes squaring numbers a lot easier, and this involves the simple trick that (hopefully) is known globally. That trick is the ”square any 2digit number that ends with a 5 in head without calculator”. Perhaps you know this trick; but for those who doesn't :

Consider this example: 35²

The (publicly known) trick is just to take the first digit: (3) and plus it by 1. (4)

3 + 1 = 4

Then multiply the first digit (3) with the 4. (3+1)

3*4 = 12

The last step is - to just 'add 25 at the end' (NOT plus!) (just write 25 at end of the answer 12) like so; 12 25

Done! You've now calculated 35² = 1225 in your head - without any calculator!

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Now to the thing I figured out - this also works for big numbers, I took (for the sake of this proof of concept) smaller numbers to begin with, and then moved up to really big numbers. And, those big numbers actually required calculator to solve.

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Now - you might be asking what the point is with this if you already have access to a calculator? And if the number is so big anyway that you need a calculator to solve it?

The point is:

What the point of the following is NOT:

It is not to solve it without calculator.

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What the point of the following IS:

The point of this is however to (hopefully) help break down a big number more easily.

And, to show you a very interesting ”chain” I found, by mistake actually! (And I just 'went with the flow')

So, Here is the ”chain” or what you’d like to call it:

2 digits = +1 at the first 1 digit:

75² =

7+1 = 8

7*8 = 56

56 and add 25 @ end: 5625

3 digits = +1 at the first 2 digits:

925² =

92+1 = 93

93 * 92 = 8556

8556 and add 25 @ end: 855625

4 digits = +1 at the first 3 digits:

8425² =

842 + 1 = 843

843 * 842 = 709806

709806 add 25 @ end:

8425² = 70980625

6 digits = +1 at the first 5 digits:

906835² =

90683+1 = 90684

90684 * 90683 = 8223497172

8223497172 and add 25 @ end:822349717225

906835² = 8.223497172×10¹ ¹

(my calculator showed this answer)

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I am currently trying to discover new ways - of doing this with another ’ending number’ that ends with something else than 5, and is larger than 100

Please, this is my first post about mathematics – If you spotted a error, tell me as soon as possible, and I will fix it! (I appreciate it, really!) Also, if you liked this: Tell me your thoughts!

If you have time, send me a review about my site, and , if you know something I could improve; tell me!.

It would be extremely helpful!

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References:

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https://en.wikipedia.org/wiki/Square_number

As I said above , You may or may not already know this trick(s) but when I first saw these (by testing out my own, just random stuff, and come across this)

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