Simplify square root of (2- square root of 5)^2+ square root of (2+ square root of 5)^2

$\sqrt{{(2 - \sqrt{5})}^{2}} + \sqrt{{(2 + \sqrt{5})}^{2}}$

Simplify each term.

Pull terms out from under the radical, assuming positive real numbers.

$2 - \sqrt{5} + \sqrt{{(2 + \sqrt{5})}^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$2 - \sqrt{5} + 2 + \sqrt{5}$

Simplify by adding terms.

Add $2$ and $2$ .

$4 - \sqrt{5} + \sqrt{5}$

Add $- \sqrt{5}$ and $\sqrt{5}$ .

$4 + 0$

Add $4$ and $0$ .

$4$