Sqrt{xsqrt[xsqrt(x)...]}=9. What is x

It's an infinite nesting of sqrt x. The answer is x=9 but I don't know why.

√x(√x(√x(√x(√x...)))) = 9

√x(√x(√x(√x(√x...))))^2 = 9^2

x*(√x(√x(√x(√x...)))) = 81..........But remember √x(√x(√x(√x(√x...)))) = 9

x * 9 = 81

x = 81/9

x = 9

Who is giving the down thumbs? The previous two respondents were correct.

If you dont get it then say so.

√(x √(x √(x √(x ... = 9

Because it is nested you can plug it into itself!
√(x * 9) = 9

If the answer is x = 9, then any sub-part of it is also 9. So try
sqrt(9sqrt(9sqrt(9sqrt(9sqrt(9sqrt(81)… which equals 9

Then try
sqrt(9sqrt(9sqrt(9sqrt(81)))
That also equal 9

So it boils down to
sqrt(81), which of course is 9

Let y=sqrt{xsqrt[xsqrt(x)...]} then

y^2=xsqrt{xsqrt[xsqrt(x)...]}=xy

y^2=xy

but y=9 since sqrt{xsqrt[xsqrt(x)...]}=9 you get y^2=81

81=9x then x=9

Given : √x(√x(√x(√x(√x...)))) = 9
square both sides
=> √x(√x(√x(√x(√x...))))² = 9²
=> x*(√x(√x(√x(√x...)))) = 81
since √x(√x(√x(√x(√x...)))) = 9
=> x ( 9) = 81
=> x = 81/9
Ans : x = 9

sqrt{xsqrt[xsqrt(x)...]} = 9
x^[(1/2) + (1/2)^2 +... + (1/2)^n +...] = 9
x = 9
---------
Attn: (1/2) + (1/2)^2 +... + (1/2)^n +... = (1/2)[1-(1/2)] = 1

Let y=sqrt{xsqrt[xsqrt(x)...]}, so that
y^2 = xsqrt[xsqrt(x)...]
=> y^2 = xy
=> x=y=9

hoiho