Simplify the Radical Expression (6 square root of 7)(7 square root of 14)

$(6 \sqrt{7}) (7 \sqrt{14})$

Multiply $(6 \sqrt{7}) (7 \sqrt{14})$ .

Multiply $7$ by $6$ .

$42 \sqrt{7} \sqrt{14}$

Combine using the product rule for radicals.

$42 \sqrt{14 \cdot 7}$

Multiply $14$ by $7$ .

$42 \sqrt{98}$

Rewrite $98$ as $7^{2} \cdot 2$ .

Factor $49$ out of $98$ .

$42 \sqrt{49 (2)}$

Rewrite $49$ as $7^{2}$ .

$42 \sqrt{7^{2} \cdot 2}$

Pull terms out from under the radical.

$42 (| 7 | \sqrt{2})$

The absolute value is the distance between a number and zero. The distance between $0$ and $7$ is $7$ .

$42 (7 \sqrt{2})$

Multiply $7$ by $42$ .

$294 \sqrt{2}$

The result can be shown in multiple forms.

Exact Form:

$294 \sqrt{2}$

Decimal Form:

$415.77878733 \dots$