Simplifying an Infinite Radical | My First Short

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[khamza]

You could also use substitution getting
sqrt(2x) =x
x^2-2x=0
x(x-2)=0
intuitively 0 is not a solution, 2 is.

[derekhasabrain]

I’m so excited to see more of your shorts, it’ll be great to see you more often!

[tbg-brawlstars]

Great !
Or just call it "x" and proceed

[xavier]

Let √2√2√2... be equal to x

x = √2√x

Squaring both sides

x² = 2√x

Again squaring both sides

x⁴ = 4x

x³ = 4

x = (4)^½

Which is cube root of 4
So x = 1.58740105197

[CoolAid]

I'm so happy that you decided to do Yt shorts. I'm looking forward to seeing more. You're my inspiration.

[AverageBishop-]

I could solve that one myself pretty quickly. Great explanation tho. Keep it up

[homayounshirazi]

infinite squre roots uner same radical approach the number under the first radical for all numbers

[parthisMC]

So what if instead of 2, it’s 2+1 for each? Such that it would be:

2^1/2 * 3^1/3 * 4^1/4 and so on

[davidseed]

another method which can be generalised.
let《》 indicare square root
if y=《x《x《x《x...》》》》
then. y²=x 《x《x《x...》》》
ie
y²=xy
y=x

[darkrai]

In this szenario, the answer would be ♾ since 2 is only approached but is never equal to the function you showed.

[alter-_-franke]

Could you also write it as √(2x) = x and then solve for x so that you get x = (0 &) 2?

[aritrachanda]

This can be solved by another method 👌

[Eduardo-zttd]

I solved with other method
= x
√(2x) = x
√2 . √x = x
x² = 2x
x² - 2x = 0
x(x-2) = 0
x = 0 or x = 2
0 is not a solution (strain solution)
So x = 2 is the solution.

[TutorOcean]

Love your content! Would you consider collaborating on a video?

[Stickman_Productions]

Dang I knew it had something to do with sums

[sohampinemath]

Nice first one to comment on this channel

[uncertifiedlinguist]

Instead of just, "we are going to write this and that this and that..."

Explain the significance of the problem. Is this problem something people usually make mistake on? What is the core concept that comes out of doing this problem.

Don't just pop up a problem and do it yourself, that is unamusing.