Simplify (2 square root of 27)*(3 square root of 32)

$(2 \sqrt{27}) \cdot (3 \sqrt{32})$

Rewrite $27$ as $3^{2} \cdot 3$ .

Factor $9$ out of $27$ .

$2 \sqrt{9 (3)} \cdot (3 \sqrt{32})$

Rewrite $9$ as $3^{2}$ .

$2 \sqrt{3^{2} \cdot 3} \cdot (3 \sqrt{32})$

$2 \sqrt{3^{2} \cdot 3} \cdot (3 \sqrt{32})$

Pull terms out from under the radical.

$2 (3 \sqrt{3}) \cdot (3 \sqrt{32})$

Multiply $3$ by $2$ .

$6 \sqrt{3} \cdot (3 \sqrt{32})$

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

Factor $16$ out of $32$ .

$6 \sqrt{3} \cdot (3 \sqrt{16 (2)})$

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

$6 \sqrt{3} \cdot (3 \sqrt{4^{2} \cdot 2})$

$6 \sqrt{3} \cdot (3 \sqrt{4^{2} \cdot 2})$

Pull terms out from under the radical.

$6 \sqrt{3} \cdot (3 (4 \sqrt{2}))$

Multiply $4$ by $3$ .

$6 \sqrt{3} \cdot (12 \sqrt{2})$

Multiply $6 \sqrt{3} (12 \sqrt{2})$ .

Multiply $12$ by $6$ .

$72 \sqrt{3} \sqrt{2}$

Combine using the product rule for radicals.

$72 \sqrt{2 \cdot 3}$

Multiply $2$ by $3$ .

$72 \sqrt{6}$

$72 \sqrt{6}$

The result can be shown in multiple forms.

Exact Form:

$72 \sqrt{6}$

Decimal Form:

$176.36326148 \dots$

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