#Help!
raven domeBOT
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elder needle
honestly idk if you can learn this it feels more like pattern recognition to me
spam questions type
elder needle
it's definitely irrational
ebon ice
So if I think in this way that root 2 + root 3, the root sign in which there is 2 + root 3
elder needle
it's definitely irrational
if it were rational you could square it and get a rational
but its square is 2+sqrt(3)
ebon ice
but its square is 2+sqrt(3)
Okay means we have to consider only 2 + sqrt(3)
elder needle
oh it does?
ebon ice
then the sqrt in which 2 + root 3 are there
what should we do with it?
I am having confusion only because of that sqrt in which there are complete eqn
ebon ice
oh it does?
..
elder needle
I am having confusion only because of that sqrt in which there are complete eqn
ok I mean you want 2 + sqrt(3) to be the square of some number right
so ideally you want something like 2+sqrt(3) = (a+bsqrt(3))^2
this is a bit bad because the RHS is going to become a^2 + 3b^2 + 2absqrt(3) which is kinda big
also there's a 2 on the sqrt(3)
so what you kinda want to do is scale the 2+sqrt(3) up a bit
red kestrel
I don't understand, where is x?
Or do you just need to evaluate some value
You can do that well using the root by hand method
And some division by decimals
radiant jackal
Are you looking for this exact type of problem to keep attempting, or just problems which contain the sqrt function? If you want all kinds of radicals to simplify, google "radical expressions", and look at the resources from there.
Anyways, the first thing you should know is what the term of this expression is, which is a "nested radical". Now, we actually have a formula to simplify this sort of radical. Do you know what it is?
radiant jackal
Actually I need to find out its irrational or not
It is not irrational. It has an answer.
gentle dune
It is not irrational. It has an answer.
it’s irrational, i checked the answer
gentle dune
this is a bit bad because the RHS is going to become a^2 + 3b^2 + 2absqrt(3) whi...
i propose a different method.
let rt(2+rt(3))=rt(a)+rt(b)
then squaring we have that a+b+2rt(ab)=2+rt(3)
this is a little more simplified as we can correlate the integer and irrational parts
@ebon ice
you can form a quadratic equation that gives values of a and b from the product and sums
using vieta’s
radiant jackal
i propose a different method.
Apologies. I seemed to have mixed up the definition for irrational. Yes, your method also works. That is exactly how I attempted the problem, before finding the formula for de-nesting. I find it to be impractical though, and I just recommend jumping straight to the de-nesting formula, since they have already done everything for you.
elder needle
i propose a different method.
I mean I was just gonna say like multiply both sides by 2 and that makes it a nice square
strong rover
this is a little more simplified as we can correlate the integer and irrational ...
if you really want to simplify it
acoustic turtleBOT
fr
strong rover
no variable only number 
analog gust
sqrt(69+sqrt(42))
strong rover
this type of
to get good at these type of questions you need to know the (a+b)^2 and (a-b)^2 formula
and that's about it
it's seldom worse like no one asks (sqrt(2)+sqrt(3)+1)^2, but any of that can be solved with simple factorization, or just being familiar with (a+b+c)^2. never are too many terms used
a good thing to remember is that if u want a+sqrt(b) to be perfect square, the radical term must have a coefficient of 2 (or any even number), only then u can think about making it a square
sometimes it'll be like
$\sqrt{19+\sqrt{192}}$
acoustic turtleBOT
fr
strong rover
but ur first step would be to see if u can take anything out of the root in the first place
strong rover
**fr**
if u cant then try to introduce a coeff of 2 like i did here
if that doesnt work
goodluck 🗣️
(theres probably some other trick)
strong rover
but like you can’t give them answers 😭
he doesnt care about the answer to this specifric problem
he wants to learn how to solve such problems
and these problems usually have a method so the best thing to do is to solve one problem for them
elder needle
fine
elder needle
so what you kinda want to do is scale the 2+sqrt(3) up a bit
I mean I was halfway to saying that anyways but like
strong rover
I mean I was halfway to saying that anyways but like
oh lmao didnt see tat
elder needle
BRUH
strong rover
wdym BRUH
strong rover
this is a bit bad because the RHS is going to become a^2 + 3b^2 + 2absqrt(3) whi...
oh the context here is algebra again
nah i wanted to provide a method without
elder needle
I mean like the intuition is basically “sub values” right
I was trying to like spell it out idk maybe that’s not the best way to explain it
ebon cosmosBOT
@ebon ice