Cube of an infinite Root

Let $y = ( \sqrt{2\sqrt{5\sqrt{2\sqrt{5\sqrt{2\sqrt{5 …}}}}}} ) ^ {3}$

$y ^ {1/3} = \sqrt{2\sqrt{5\sqrt{2\sqrt{5\sqrt{2\sqrt{5 …}}}}}}$

$y ^ {1/3} = \sqrt{2\sqrt{5 y ^ {1/3}}}$

Squaring both sides:

$y ^ {2/3} = 2 * \sqrt{5 y ^ {1/3}}$

Squaring again both sides:

$y ^ {4/3} = 4 * 5 y ^ {1/3}$

$y = 20$

$Answer = \boxed{20}$