Evaluate 3 square root of 12*(5 square root of 6)

$3 \sqrt{12} \cdot (5 \sqrt{6})$

Step 1

Rewrite $12$ as $2^{2} \cdot 3$ .

Factor $4$ out of $12$ .

$3 \sqrt{4 (3)} \cdot (5 \sqrt{6})$

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

$3 \sqrt{2^{2} \cdot 3} \cdot (5 \sqrt{6})$

$3 \sqrt{2^{2} \cdot 3} \cdot (5 \sqrt{6})$

Step 2

Pull terms out from under the radical.

$3 (2 \sqrt{3}) \cdot (5 \sqrt{6})$

Step 3

Multiply $2$ by $3$ .

$6 \sqrt{3} \cdot (5 \sqrt{6})$

Step 4

Multiply $6 \sqrt{3} (5 \sqrt{6})$ .

Multiply $5$ by $6$ .

$30 \sqrt{3} \sqrt{6}$

Combine using the product rule for radicals.

$30 \sqrt{6 \cdot 3}$

Multiply $6$ by $3$ .

$30 \sqrt{18}$

$30 \sqrt{18}$

Step 5

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

Factor $9$ out of $18$ .

$30 \sqrt{9 (2)}$

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

$30 \sqrt{3^{2} \cdot 2}$

$30 \sqrt{3^{2} \cdot 2}$

Step 6

Pull terms out from under the radical.

$30 (3 \sqrt{2})$

Step 7

Multiply $3$ by $30$ .

$90 \sqrt{2}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$90 \sqrt{2}$

Decimal Form:

$127.27922061 \dots$

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