Evaluate 2 square root of 7x*3 square root of 14x^2

$2 \sqrt{7 x} \cdot 3 \sqrt{14 x^{2}}$

Reorder $14$ and $x^{2}$ .

$2 \sqrt{7 x} \cdot (3 \sqrt{x^{2} \cdot 14})$

Pull terms out from under the radical.

$2 \sqrt{7 x} \cdot (3 (x \sqrt{14}))$

Multiply $2 \sqrt{7 x} (3 x \sqrt{14})$ .

Multiply $3$ by $2$ .

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

Combine using the product rule for radicals.

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

Multiply $14$ by $7$ .

$6 (x \sqrt{98 x})$

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

Factor $49$ out of $98$ .

$6 (x \sqrt{49 (2) x})$

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

$6 (x \sqrt{7^{2} \cdot 2 x})$

Add parentheses.

$6 (x \sqrt{7^{2} \cdot (2 x)})$

Pull terms out from under the radical.

$6 (x (7 \sqrt{2 x}))$

Simplify the expression.

Rewrite using the commutative property of multiplication.

$6 (7 x \sqrt{2 x})$

Multiply $7$ by $6$ .

$42 x \sqrt{2 x}$