Simplify square root of square root of 8

$\sqrt{\sqrt{8}}$

Step 1

Rewrite $8$ as $2^{2} \cdot 2$ .

Factor $4$ out of $8$ .

$\sqrt{\sqrt{4 (2)}}$

Rewrite $4$ as $2^{2}$ .

$\sqrt{\sqrt{2^{2} \cdot 2}}$

Step 2

Pull terms out from under the radical.

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

Step 3

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$1.68179283 \dots$