If $\sqrt{6+4\sqrt2} = x+\sqrt x$ , find the value of $x^6$ .

The answer is 64.

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$\sqrt{6+4\sqrt{2}} = \sqrt{2} \cdot \sqrt{3+2\sqrt{2}} = \sqrt{2} \cdot \sqrt{(1+\sqrt{2})^{2}} = \sqrt{2} \cdot (1+\sqrt{2}) = 2 + \sqrt{2}$

$x = 2$

$x^{6} = 64$