Evaluate 4 square root of 10*(3 square root of 6)

$4 \sqrt{10} \cdot (3 \sqrt{6})$

Multiply $4 \sqrt{10} (3 \sqrt{6})$ .

Multiply $3$ by $4$ .

$12 \sqrt{10} \sqrt{6}$

Combine using the product rule for radicals.

$12 \sqrt{6 \cdot 10}$

Multiply $6$ by $10$ .

$12 \sqrt{60}$

$12 \sqrt{60}$

Rewrite $60$ as $2^{2} \cdot 15$ .

Factor $4$ out of $60$ .

$12 \sqrt{4 (15)}$

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

$12 \sqrt{2^{2} \cdot 15}$

$12 \sqrt{2^{2} \cdot 15}$

Pull terms out from under the radical.

$12 (2 \sqrt{15})$

Multiply $2$ by $12$ .

$24 \sqrt{15}$

The result can be shown in multiple forms.

Exact Form:

$24 \sqrt{15}$

Decimal Form:

$92.95160030 \dots$

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