Question

$\sqrt{2 \sqrt{2 \sqrt{2 \sqrt{2 \sqrt{2 \sqrt{?} } } } } }$

Answer 1

x  = √( 2 * √( 2 * √( 2 * √(2 * √( 2 * .....)))))
=> x  = √( 2 x )
=> x²= 2 x
=> x² - 2 x = 0
=> x ( x - 2 ) = 0
=> x = 0   or   x - 2 = 0
=> x = 0 , 2 .
 So x can be both, zero and two.
There is no reason for zero not to be a root. Both, two and zero, satisfies the equation.