Proof that x=sqrt(x(sqrt(x ......))) dx

In this video, I showed how to evaluate a nested radical product of x as equal to x

[tunchimelo]

Keep it up with the good works sir .God bless you abundantly ❤

[plyiz]

Thanks, man you uploaded this at just the right time. Can I contact you ( I would do this rarely) when I am stuck on a particular problem?

[kinanradaideh]

What if we plugged in X back into the square root so we get X = sort(X*X) = sqrt (X^2) = |X|.
In this case we prove that X = |X|. Is that enough?

[natureandus]

Let t=sqrt(xsqrt(…)). Then t=sqrt(xt) and so t^2=xt. t(t-x)=0. t=0 or t=x. ….