Simplify square root of square root of square root of 625

$\sqrt{\sqrt{\sqrt{625}}}$

Rewrite $625$ as $25^{2}$ .

$\sqrt{\sqrt{\sqrt{25^{2}}}}$

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

$\sqrt{\sqrt{25}}$

Rewrite $25$ as $5^{2}$ .

$\sqrt{\sqrt{5^{2}}}$

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

$\sqrt{5}$

The result can be shown in multiple forms.

Exact Form:

$\sqrt{5}$

Decimal Form:

$2.23606797 \dots$