Simplify square root of 8a^2* square root of 4a

$\sqrt{8 a^{2}} \cdot \sqrt{4 a}$

Rewrite $8 a^{2}$ as ${(2 a)}^{2} \cdot 2$ .

Factor $4$ out of $8$ .

$\sqrt{4 (2) a^{2}} \cdot \sqrt{4 a}$

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

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

Move $2$ .

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

Rewrite $2^{2} a^{2}$ as ${(2 a)}^{2}$ .

$\sqrt{{(2 a)}^{2} \cdot 2} \cdot \sqrt{4 a}$

$\sqrt{{(2 a)}^{2} \cdot 2} \cdot \sqrt{4 a}$

Pull terms out from under the radical.

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

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

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

Pull terms out from under the radical.

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

Multiply $2 a \sqrt{2} (2 \sqrt{a})$ .

Multiply $2$ by $2$ .

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

Combine using the product rule for radicals.

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

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

Reorder factors in $4 a \sqrt{a \cdot 2}$ .

$4 a \sqrt{2 a}$

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