Multiplying numbers using square numbers.

To do this, you have to know a lot of square numbers. You can look up a list online if you want. All that is needed is to take the square of the average of the two numbers, then subtract by the square of the amount of numbers away from the average the two are. For example, given 51x45, the average is 48, and they are 3 numbers away from it. The square of 48 is 2,304 and the square of 3 is 9. Subtract the two numbers to get your answer, 2,295. I have to manually count -1 for this number, +1 for that over and over to get the average number and the distance from it, maybe you can do it quicker. For that reason, it's the quickest if the 2 numbers are close to each other.

So far this only works if the numbers are either both even or both odd so that the average number is an integer, a number without decimals. It probably works if this isn't true, but it involves fractions and is more complicated.

Also, remember my previous post about multiplying one number by something and dividing the other by the same amount, if your two numbers are far apart and you want to make them closer. This is a link to the first thousand squares, which leads to one million. Also, I admit, I cheated a little on this one. I noticed that the pattern was 1 different for the first number, 3 more different for the second, 5 more for the third, 7... and I didn't realize that this was a square as well, and so I has some help on Quora. Also, the +1 formula I posted in 2012 is similar to this, it just involved one, though.

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March Seventeenth, 2019

I found (also on Quora) a way to multiply two-digit squares. A summary: Take the last digit, square it. Then multiply the first and last digits, then double that number. Then square the first number. Now you have three numbers. Place them in order, from right to left. Then combine them into one by adding, as the first number is in the ones place, the second is in the tens and the third is in the hundreds. If you want examples, they're in the comments.The two digits could be anywhere, including a number like 1.6, since you can just multiply numbers, ignoring periods, calculating them at the end of the process. Since the square method has a 50% chance of ending in .5 if you started with whole numbers (if the two numbers had differing parities), I'll try to find a method for multiplying 3-digit numbers.

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The Next Day

Today, I calculated the results when squaring numbers ending in .5. 1.5, 2.5, 3.5, etc. When I subtracted by the non-decimal portion squared (As in, 7.5²-7²), I got the number (7 in the example) +.25 as the result. So now, you can multiply any two digit numbers in your head!

Square Root Omniscience

14 = 3.5 x 4, which are the closest numbers I know of that equal it. If you want to take the square root of 14, the answer is between those 2. The closer the numbers to each other, the more exact the square root. The actual number is 3.741657387, which is slightly less than the average, the halfway point. If you take another number that has 2 numbers half a number away, like 33=5.5x6, the square root is almost the same, 3.744562647. The numbers grow father away from the halfway point the farther from each other they are, as follows:

√48 (6x8) = 6.92820323
√30 (6x5) = 5.477225575
√180 (15x12) = 13.41640
786