This method is even more effective if you memorize all the squares up to 100. So instead of the square root of 19, I'd add two zeroes and take the square root of 1900. 43^2 is 1849, and 44^2 is 1936, so the first two digits are 43 (I can place the decimal point at the end). 1900 is 51/97 of the way between 43 and 44, and by inspection I can see that the next digit is a 5. So I already know the answer starts with 4.35. A linear approximation begins to deviate from the true value after we double the number of significant digits, so I use this method to go from three digits to six digits, then from six digits to twelve digits, etc. And... I do it all in my head.
This method does not work when the value is far away from previous square. Try this method for 13 or 99, for example. What is the point in multiplying by 1/2...
This method works for numbers that are close to ANY perfect square, not just the previous perfect square. You just have to go the opposite direction. In your case with 99, the approximation would be sqrt(99) = 10 + (-1)/(10*2) = 9.95, which is close to its actual value 9.94987437.
We just found this video tonight and my family wanted to express our thanks for this method. As soon as my guy watched you do it, he rushed back to his homework and started cranking. Having two examples also makes it easier to follow your logic. Very well done.
Since calculating in my head is easier for me I find how many steps it is from 16 to 25 (9), subtract 16 from 19 and the fraction value is 3/9 or .333. Add that to 4 and you get an approximation of 4.333.
Hey I'm curious about how did you made that, that you write on whiteboard and at the same time we can see it from opposite perspective? did you learned to write in reverse or something?
It always drove me crazy that none of my math teachers ever gave me a method to find a square root without a calculator. This method is super helpful, but it still requires you to memorize perfect squares though. I really just want a formula for finding the square root of any number.
I got here because I'm trying to find out if it's possible getting the square root of a number without a calculator and I can't really use this because I'm dumb or it's just too advance for me lol First I don't know how to divide something like 3÷8 maybe 8÷3 like 2.33? (That took me several seconds and it's wrong I check the calculator) The best I can do that took couples of second will be 3+3 and 15+17 and 135+57 which took several seconds and I tried to do a hard one like 135×57 my answer is 7,435 and it's wrong and it took almost 4 minutes lol And the video said find the perfect square root of the number so how am I going to find the nearest square root of 7,695? Lol I guess this only works on 2 to 3 digit numbers or someone that was just very good at math My mental math will be average at best and I guess this will not be a problem unless in the future that we need to somehow solve a calculus problem without calculators or formulas lmao (I hope I just did not jinx myself because I'm definitely screwed if that happens)
To get a ballpark guesstimate of the closest perfect square i think one could just calculate squares for a few numbers to triangulate. Like for 7435, that’s close ish to 100^2, whcuh is 10000, so its own root is less than 100. 50^2 is 2500, clearly too low so how about 80^2, that’s 6200, getting closer, 90^2 is 8100, too high but closer. So now let’s try to get precise, 85^2 is…more math but not crazy…7225 closer still and only off by 210… so let’s try 87^2…7569… too high…so Let’s try 86 to see if it’s closer than 85. 86^2 = 7396. That’s the closest perfect square to 7435.
I don't really remember much, but I think it's one of the applications of calculus; derivation to be precise. Just check it up and you'll see how it's solved using calculus. But that one is a bit more technical and won't be so easy to rmr
@@donarthiazi2443 Consider (a+b)^2 = a^2 + 2ab + b^2. "a" is the "big number", the 4, or the 5. "b" is what's left over. once that squared is subtracted, as he has. So what is b? If we think of what is left as 2ab, you can compute b as he has. "Close enough".
Invert principle >> go next higher square root instead of lower. So the square root of 16 is 4, which leaves 1 [16 minus 15], 1 divided by 4 times half [0.5] = 0.125, then instead of adding to original square root, deduct it from 4, which leaves 3.875. So 3.875 times 3.875 id 15.016, close enough.
