Conjugation on limit

Calculus Level 1

limx(x+xx),limx(x+x+xx) \large \lim_{x\to\infty}\left( \sqrt{x +\sqrt{x}} - \sqrt{x}\right), \quad \lim_{x\to\infty}\left( \sqrt{x +\sqrt{x +\sqrt{x}}} - \sqrt{x}\right)

It is possible to show that both the limits above are equal to 12. \frac12.

Is it true that the limit below is also equal to 12? \frac12?

limx(x+x+x+xx) \lim_{x\to\infty}\left(\sqrt{x+ \sqrt{x +\sqrt{x +\sqrt{x}}}} - \sqrt{x}\right)

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