Simplify square root of 32* square root of 2

$\sqrt{32 \cdot \sqrt{2}}$

Step 1

Rewrite $32 \cdot \sqrt{2}$ as ${(2^{2})}^{2} \cdot (2 \cdot \sqrt{2})$ .

Factor $16$ out of $32$ .

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

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

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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

Step 3

Raise $2$ to the power of $2$ .

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$6.72717132 \dots$