Simplify 6 square root of 2*5 square root of 14

$6 \sqrt{2} \cdot 5 \sqrt{14}$

Multiply $6 \sqrt{2} (5 \sqrt{14})$ .

Multiply $5$ by $6$ .

$30 \sqrt{2} \sqrt{14}$

Combine using the product rule for radicals.

$30 \sqrt{14 \cdot 2}$

Multiply $14$ by $2$ .

$30 \sqrt{28}$

$30 \sqrt{28}$

Rewrite $28$ as $2^{2} \cdot 7$ .

Factor $4$ out of $28$ .

$30 \sqrt{4 (7)}$

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

$30 \sqrt{2^{2} \cdot 7}$

$30 \sqrt{2^{2} \cdot 7}$

Pull terms out from under the radical.

$30 (2 \sqrt{7})$

Multiply $2$ by $30$ .

$60 \sqrt{7}$

The result can be shown in multiple forms.

Exact Form:

$60 \sqrt{7}$

Decimal Form:

$158.74507866 \dots$

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