Limits of square root $$\lim_{x\to\infty}\left(\sqrt{x+\sqrt{x+\sqrt{x + \sqrt x} }}-\sqrt x\right) $$
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Compute the limit
Can you please help me out with this limit problem

Hint for a simpler one:  $$\lim_{x \to \infty} \sqrt{x+\sqrt x}-\sqrt x=\lim_{x \to \infty}\sqrt x\left(\sqrt{1+\frac 1{\sqrt x}}-1\right)$$
