I just tested this method and it's quite impressive. For numbers 4 - 1000: error is 0.171573 max, 0.00000 min, 0.009804 avg Also confirm the loss of precision arround the perfect square roots. Thanks.
If accuracy isn't important, then it can also help to learn to squares of every half number (1.5, 2.5, 3.5, ...). These squares are easy to learn by a little trick. Take the whole number before the decimal point and multiply it with the next whole number. After that add 0.25. So f.e. 7.5^2= 7*8+0.25 = 56.25. With the example of root 42 I immidiatly knew the answer would be just under 6.5. This method is very quick in estimating roots, but is ofcourse less reliable for answers around x.25 and x.75. Another benifit for learning these squares is that you'll learn the squares for 15, 25, 35, ... at the same time.
One method I personally find easy for myself is starting with finding the closest perfect square to 42, which in this case is 6^2 = 36, then subtracting 36 from 42 (42-36 = 6) after the subtraction, divide the difference with the square root of 36 times 2 (6 • 2) and lastly add the difference with the quotient and you get a pretty close answer. That means 6/12 is 0.5 0.5 + 6 = 6.5 6.5^2 ≈ 42 Awesome video by the way! Keep uploading because you’ve definitely gotten me as a new subscriber!❤️
I actually think that the former video is more useful for me. When I need a square root and I can't use a calculator it's usually due to being in a biolab and wearing gloves. And this method might be nice for getting somewhere into the ballpark, but I might need to decide how many milli- or microliters/grams of a solution or substance I should use and this method simply doesn't cut it in some cases. Each method has its applications.
Hi, Science Vigilante Steve over here.. . I can't remember enough about that 4 function calculator algorithm to say. I just seem to remember that as you did more and more iterations, you got more and more significant digits. I don't recall having to write anything. I also don't recall if it oscillated up and down, or slowly approached from one side while converging. I'd purely guess it oscillated. . . It may have needed the single Memory register to save intermediate results because you destroyed the previous guess, but again, can't recall much. . . I checked an old file drawer thinking I may have written it down, but only found my 1966 military immunization record, a picture of a nameless girl I'm sure I liked probably in highschool, and our wedding rings' receipt from 1969. . .
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
Isn't it way easier to calculate the decimal by saying 42 is 6/13 of the way from 36 to 49. (49-36=13, 42-36=6). Then you get 6 6/13 = 6.46. seems close enough for me.
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.
This IS easier than your first method. But you missed that 39 and 6 can both factor out a 3 and seemed a bit sluggish when making this one. Did you take your meds just before filming? ;)
I appreciate what you are doing on your videos. The way I came across your video was the search of how my professor would calculate square root. I haven't found anything yet. If you were standing beside him with a calculator. I could give you the number 746397. By the time you entered it and git the square root. He would already have the answer up to 4 or 5 places. Never have figured it out.
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 just tested this method and it's quite impressive.
For numbers 4 - 1000:
error is 0.171573 max, 0.00000 min, 0.009804 avg
Also confirm the loss of precision arround the perfect square roots.
Thanks.
Thank you very much for your extensive comment!
If accuracy isn't important, then it can also help to learn to squares of every half number (1.5, 2.5, 3.5, ...). These squares are easy to learn by a little trick.
Take the whole number before the decimal point and multiply it with the next whole number. After that add 0.25. So f.e. 7.5^2= 7*8+0.25 = 56.25.
With the example of root 42 I immidiatly knew the answer would be just under 6.5. This method is very quick in estimating roots, but is ofcourse less reliable for answers around x.25 and x.75.
Another benifit for learning these squares is that you'll learn the squares for 15, 25, 35, ... at the same time.
Nice one!
One method I personally find easy for myself is starting with finding the closest perfect square to 42, which in this case is 6^2 = 36, then subtracting 36 from 42 (42-36 = 6) after the subtraction, divide the difference with the square root of 36 times 2 (6 • 2) and lastly add the difference with the quotient and you get a pretty close answer.
That means 6/12 is 0.5
0.5 + 6 = 6.5
6.5^2 ≈ 42
Awesome video by the way! Keep uploading because you’ve definitely gotten me as a new subscriber!❤️
Interesting method. You're right about the video. This one is better than the other plus you have something new to me to check out. Love it!
Glad it was helpful!
you could have simplified 39/6 to 13/2 and 104/14 to 52/7 and saved some pain
I actually think that the former video is more useful for me.
When I need a square root and I can't use a calculator it's usually due to being in a biolab and wearing gloves. And this method might be nice for getting somewhere into the ballpark, but I might need to decide how many milli- or microliters/grams of a solution or substance I should use and this method simply doesn't cut it in some cases.
Each method has its applications.
Fair enough!
Thanks for the video 👍
Hi, Science Vigilante Steve over here.. . I can't remember enough about that 4 function calculator algorithm to say. I just seem to remember that as you did more and more iterations, you got more and more significant digits. I don't recall having to write anything. I also don't recall if it oscillated up and down, or slowly approached from one side while converging. I'd purely guess it oscillated. . . It may have needed the single Memory register to save intermediate results because you destroyed the previous guess, but again, can't recall much. . .
I checked an old file drawer thinking I may have written it down, but only found my 1966 military immunization record, a picture of a nameless girl I'm sure I liked probably in highschool, and our wedding rings' receipt from 1969. . .
Haha 😂
So how do a computer actually calculate square root? Are they using the method you have shown in older video?
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
It would have been far easier to simply divide 78 by 12, which equals 6.5! You added an extra step.
:O this is so easy! thanks!
Nice 😌 one here
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
Isn't it way easier to calculate the decimal by saying 42 is 6/13 of the way from 36 to 49. (49-36=13, 42-36=6). Then you get 6 6/13 = 6.46. seems close enough for me.
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.
This IS easier than your first method. But you missed that 39 and 6 can both factor out a 3 and seemed a bit sluggish when making this one. Did you take your meds just before filming? ;)
Check the bottom right of the screen for the time-and no, I hadn’t taken my ADHD medication.
looks like the same method as below, you may be interested to compare among them.
ruclips.net/video/VrQF_DFndO8/видео.html
I appreciate what you are doing on your videos. The way I came across your video was the search of how my professor would calculate square root. I haven't found anything yet. If you were standing beside him with a calculator. I could give you the number 746397. By the time you entered it and git the square root. He would already have the answer up to 4 or 5 places. Never have figured it out.
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.