Simplify square root of 2 square root of 8

$\sqrt{2 \sqrt{8}}$

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

Factor $4$ out of $8$ .

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

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

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

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

Pull terms out from under the radical.

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

Write the expression using exponents.

Multiply $2$ by $2$ .

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

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

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

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

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:

$2.37841423 \dots$

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