@fermatslibrary Looks like damping the function f(x) = sqrt(x) so it converges, then iterating to find the fixed point. A fundamental technique taught early in #sicp 🙂 (fixed-point (average-damp (...)) See:

@fermatslibrary Here is another useful trick: Take whatever method works best for you und approximate every square root before you use the calculator. That way you get the necessary practice and it will come in really handy once you got the hang of it ;)

@fermatslibrary @mewelch11 suing these guys for copyright infringement

@fermatslibrary 1. Try to remember this method 2. Fail, ask Siri 3. Grab a calculator while waiting for a response and yep ok Siri says I found this on the web for “where is the square root of pants lasagna”

@fermatslibrary i say another simple method. . take approx squre root of 17 i. e 4 . . Divide 17/4 = 4.25 . then take avg of 4.25 and 4, u will get 4.125 simple?

@fermatslibrary Newton-Raphson FTW

@fermatslibrary This is also known as the Newton-Raphson Method. In this case, f(x) = x^2 - 17, f'(x) = 2x and the x0 = 4.

@fermatslibrary when I need to, I just add to x the result of 1 divided by the difference of the power of x and x+1 and then multiplied by the difference between x and y. Sqrt(20): 4+4*[1/(25-16)] = 4+4*(1/9) = 4.444 Of course, the bigger the number the finest the results

@fermatslibrary This is the method that mathematicians would devise ‘from first principles’; however, I once saw a method that looked like long division which I think is more user friendly.

@fermatslibrary use a calculator. No y do u require root 17? @monsoon0 @Meetasengupta

@fermatslibrary That's called Newton- Raphson method

@fermatslibrary This is also half of the Newton iteration method which if you collect enough public keys from devices can quickly crack the weak keys where any two share the same prime factor. Hint, never trust a cheap embedded device to generate secure RSA key-pairs.

@fermatslibrary HMPH

@fermatslibrary I remember learning this in school (since forgotten) written out like long division.

@fermatslibrary Awesome. Wish I had this when I had to do square roots by hand in high school.

@fermatslibrary ☝️☝️☝️ you're welcome, atau udah tau? @asardeni

@fermatslibrary @elonmusk but the quickest method is to use the calculator 😂

@fermatslibrary Why not simply follow the long division method which provides accurate answers to as many decimals as you’d want? Incidentally, the steps are similar as well.

@fermatslibrary I was taught how to calculate a square root exactly in the first year of my secondary school. #1971