The key is that a+b needs to be positive, or else you need to have a+b-sqrt(ab); a classic example of getting mixed up by taking the wrong square root!
I was doing homework for my math course and I encountered these nested square roots and I had to simplify it the long way(solving quadratics and stuff). Thanks bprp!
Neat. I would have never thought of approaching these problems in this way, and I don't remember learning it in algebra, though I could have just forgotten. I tend to just approximate whenever i see a root these days, so that I don't need to reach for a calculator so often.
I remember learning nested square roots from you over 6 years ago Back then, when our highschool teacher gave us a nested square root for the first time, I was able to solve it quickly while everyone else had no idea what to do with it lol (I was far from being a top student, so it was quite a fun sight) Now I’m a grad student and nostalgia drives me back to your channel 😊
I have carefully observed how the amazing marker switch works, Your current pen us held in between your hand and index finger plus other matker and the offside marker is held with thumb facing left(or pretty much on the left) and the ON marker is on the right to hold it. to switch, flick up your thumb and flick down your index finger and adjust if needed.
you could just separate it into 2 * 3.5 and than turn 7√b into 2√(3.5²b) = 2√(12.25b) but as you can see, this creates either decimals or fractions, which makes the rest of the calculations cumbersome.
@@pritamdas5439 I wanna know if there's a faster and more efficient way like how he showed the synthetic division method vs long division method for polynomials
@@anassayed2077 It came from 9th century Arabic, from Persian mathematician Muhammad ibn Musa al-Khwarizmi, from whence we also get the word "algorithm."
While I agree, that it is a nice 'shortcut', it is essentially useless information and equivalent to me telling someone from Australia, that there is a shortcut in my backyard in Germany. Hardly ANYONE will ever be in a place to use it ONCE, let alone regularly.
@m.h.6470 and how does that relate to it being a nice shortcut? It was never argued that this was useful. I can read, i am just confused as to why you're making a point about something that was never implied. You seem to be complaining about non-existent things.
@@一_一一一一一一一一 A nice shortcut that is never used is pointless. That was the entire reason for my comment. 99.9% of viewers will NEVER be in a situation, where this shortcut is relevant or useful, so this shortcut and therefore the video is pointless.
It is not useless, it is common sense and quite useful. If a irrational number is in form √[a+b+√(ab)] It can be written as √[(√a)²+(√b)²+2•√a√b]. =√(√a+√b)² =√a+√b
