Find Square Roots w/o Calculator by Hand Quickly & Easily 

Thank you very much for your extensive comment!

Nice one!

Fair enough!

Glad it was helpful!

Haha 😂

Neither. Take a look at this Quora thread where about 100 different ways computers can do it: How do computers calculate square roots? - Quora www.quora.com/How-do-computers-calculate-square-roots

I timed your method and mine with 20 different non-perfect squares and both methods took about the same time and both were equally accurate-so yes 👍 👏-I like your method! I’ll show the kids and see what they think and let them use your method if they like it more. Thank you! Note: There is a problem with your method-but it only starts to reveal itself as the numbers get bigger: Your method is “linear” and only works if the roots are more or less equally spaced apart-but they aren’t, not at all, and as the two perfect roots flanking your non-perfect-root number get larger, your method produces increasingly less accurate results until, once the numbers get up above 500 or 1,000, this method produces answers which are 70-90% wrong. I’m not bashing you-like I said-for relatively small numbers, it’s great 👍.

@@AthenianStranger yes, you're right. When I thought of this, I only really considered smaller numbers since I thought most average people wouldn't know the higher number perfect roots. Good to know you tested it and actually calculated the accuracy.

I can sort of explain the method-your professor was 95% just a genius-but the other 5% is kind of a trick of numbers and how they’re actually put together + a truly prodigious memory of perfect squares. You only need to look at the first and last couple of digits and count how many digits there are to figure out which of about 17 different routes to take, and then, *very very very quickly you mentally add up all the numbers to get the “digital sum” (e.g. 71945 is 7 + 1 + 9 + 4 + 5 = 26) and then you add the digits of the “digital sum” to get the “digital root” which in this example is 2 + 6 = 8. Alright, now comes the ridiculously large memory bank part. Your professor figures “it’s a six digit number so that’s the hundreds of thousands-hmm…I know 8 * 8 is 64 so 800 * 800 (6 total digits) is 640,000-too small; likewise, 9 * 9 is 81 so 900 * 900 (6 total digits) is 810,000 which is too high-so he already knows the whole number part of the root of 746,379 is three digits long and it’s between 800 and 900…but closer to 900…just like is closer to 81 than 64. But how close? Well-it’s gotta be bigger than 850, so now he’s thinking the root is 8 6 _ . Just needs the last digit. Remember before we found the “digital root” was 8? The square root of 8 is almost 3. So maybe it’s 863.” The actual square root is approximately 863.94. So, now you know it’s not “insanely ridiculously difficult” but WOW 😮 that is A LOT OF MENTAL MATH. And there some old dudes in the comments who have even more clever tricks than this. So again, professor-mad lad level genius-but also just playing a bit of a game and doing an insane amount of mental math and, if you memorize all squares and roots up to 100 (that’s only 200 flash cards-you spend an hour a day running through them for a year or two and they will be memorized in long term instantaneous recall memory. Once you know your double-digit squares and roots you can basically find the square root of any number because we’re on a base 10 system so those perfect roots just get more and more zeroes added to them the bigger the number of digits gets. The only other thing that matters is the total number of digits and do the little digital root adding trick. Then you look at the first couple digits and follow the above pattern of steps and you can be a “human calculator” too. Like I mentioned-roll the comments and you’ll find some old ex-military flight navigator dudes who were taught much better and more clever and faster tricks than what I just demonstrated. The point is-it isn’t magic-it’s memorization, practice, and a “head for numbers” (people who are just super good at mental arithmetic). I am not one of those people so I am as amazed as you are at people who can do all that stuff in their heads.

@@AthenianStranger all of the students tried to get him to reveal his secret. Like I said. He was dead on the money every time. It got to a point we quit asking.

I like the way you are organised

I sincerely appreciate your kind compliments!

As a left-handed person, it's either be OCD-level organized or your paper looks like it's slowly turning into a whirlpool.

@@AthenianStranger really

Check the bottom right of the screen for the time-and no, I hadn’t taken my ADHD medication.