Simplify square root of fourth root of 4

$\sqrt{\sqrt[4]{4}}$

Step 1

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

$\sqrt{\sqrt[4]{2^{2}}}$

Step 2

Rewrite $\sqrt[4]{2^{2}}$ as $\sqrt{\sqrt{2^{2}}}$ .

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

Step 3

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

$\sqrt{\sqrt{2}}$

Step 4

Rewrite $\sqrt{\sqrt{2}}$ as $\sqrt[4]{2}$ .

$\sqrt[4]{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\sqrt[4]{2}$

Decimal Form:

$1.18920711 \dots$