Simplifying a Radical | Denesting
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- Опубліковано 20 жов 2024
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The topic of de-nesting roots is exhaustively solvable. Given √(a±√b), if we set D = a²-b then it will de-nest if and only if D is a perfect square of a rational number. If it is, the solution is √x±√y where x = a/2+√(D/4), y = a/2-√(D/4). It's an analog for "quadratic formula" if you wish. This trivializes any de-nesting problem to just substituting coefficients, checking the discriminant and solving it - much like in case of quadratic equation. I'll leave it for those who've read this as to why this formula and the statement is true.
Each of these methods are simply great. Nice work!
Here I propose a forth method:
I realized that 3/2-✓2 can be written as: 1+1/2-✓2 or 1+1/2-2/✓2 which is easy to identify as a perfect square: (1-1/✓2)^2.
I got inspired by something you did recently to obtain a perfect square by adding and subtracting 1 if I remember correctly. Not exactly the same but similar.
Thanks again for your "maths moments".
3 methods are so cool to simplify a radical! Especail the 3rd method, this is my first time see. 👍👍👍👍👍👍
you couldv'e said the 3 methods are radical
Very nice as well very educational!👍✌️👍
Great job !! 👍👍
Amazing! 👏👏👏💐
It highly depends on input expression, sometimes calculation can be complex
I did it as the 2nd method.
Brilliant!
at 9:13 he incorrectly wrote the second term for the y equation , it should be + sqroot 2 but got the right result anyway, Me laughing!
1 and 2 metods are the same - completing the square!
I used the second method, except my signs somehow flipped.
Ans _ 1-(1/√2)
1 - rt ( 0.5)
👍
1.5-1.414=0.086
and the root???
(2-√2)/2
Sqrt of 2 is approx. 1.414. After taking it away from 1.5 we get 0.0857. This is like 857/10000. So what's the square root of a number like that? Well, it's "almost" like 30/100 (a bit less), so 0.3 (vs. around 0.29289) is a pretty fair approximation I think :-). No need to spend 10 minutes doing the complex math stuff... Around 10 seconds is enough to approximate.
What for??? Nested radicals formula is written on each and every wall. en.wikipedia.org/wiki/Nested_radical
For exercizing your brain purposes
Looking at all my nearby walls, none have any formulae written on them. Do you have a graffiti problem in your neighborhood?
@@Qermaq Change the walls :).
@@MichelLafer Reinventing standard formulas is a kind of running on the spot. Better he finds more tasks like Sum k=1 to 2021 (k^2+3k+1)k! He could at least do it in general form -✓(a--✓b)
@@vladimirkaplun5774 I called a few contractors to renovate my walls, and I can't decide. Can you help?
Euclid Construction can only do the job but only if all the walls are perfectly flat.
Hamilton Builders will build in 3-space but they are hard to work with.
Graham's Home Solutions just wants to add trees everywhere.
I called Discreet Math Projects, but they only do floors and ceilings.
And apparently the Wallis Product has nothing to do with walls, it's just his name dammit.