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Combine 3 square root of 27*(3 square root of 6)

$3 \sqrt{27} \cdot (3 \sqrt{6})$

Step 1

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

Factor $9$ out of $27$ .

$3 \sqrt{9 (3)} \cdot (3 \sqrt{6})$

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

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

Multiply $3$ by $3$ .

$9 \sqrt{3} \cdot (3 \sqrt{6})$

Step 4

Multiply $9 \sqrt{3} (3 \sqrt{6})$ .

Multiply $3$ by $9$ .

$27 \sqrt{3} \sqrt{6}$

Combine using the product rule for radicals.

$27 \sqrt{6 \cdot 3}$

Multiply $6$ by $3$ .

$27 \sqrt{18}$

$27 \sqrt{18}$

Step 5

Rewrite $18$ as $3^{2} \cdot 2$ .

Factor $9$ out of $18$ .

$27 \sqrt{9 (2)}$

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

$27 \sqrt{3^{2} \cdot 2}$

$27 \sqrt{3^{2} \cdot 2}$

Step 6

Pull terms out from under the radical.

$27 (3 \sqrt{2})$

Step 7

Multiply $3$ by $27$ .

$81 \sqrt{2}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$81 \sqrt{2}$

Decimal Form:

$114.55129855 \dots$

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