# Let sqrt(1 + sqrt(3 + sqrt(5+ sqrt(x)))) = 2 What x?

Apr 26, 2016

$x = 961$

#### Explanation:

$\sqrt{1 + \sqrt{3 + \sqrt{5 + \sqrt{x}}}} = 2$

or $1 + \sqrt{3 + \sqrt{5 + \sqrt{x}}} = 4$

or $\sqrt{3 + \sqrt{5 + \sqrt{x}}} = 3$

or $3 + \sqrt{5 + \sqrt{x}} = 9$

or $\sqrt{5 + \sqrt{x}} = 6$

or $5 + \sqrt{x} = 36$

or $\sqrt{x} = 31$ or $x = 961$