Simplify square root of square root of 32

$\sqrt{\sqrt{32}}$

Rewrite $32$ as $4^{2} \cdot 2$ .

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Factor $16$ out of $32$ .

$\sqrt{\sqrt{16 (2)}}$

Rewrite $16$ as $4^{2}$ .

$\sqrt{\sqrt{4^{2} \cdot 2}}$

Pull terms out from under the radical.

$\sqrt{4 \sqrt{2}}$

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

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

Pull terms out from under the radical.

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

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

$2 \sqrt[4]{2}$

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt[4]{2}$

Decimal Form:

$2.37841423 \dots$

Simplify square root of square root of 32

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