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

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

Multiply $3$ by $7$ .

$2 \sqrt{21 x \sqrt{14 x^{2}}}$

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

$2 \sqrt{21 x \sqrt{x^{2} \cdot 14}}$

Pull terms out from under the radical.

$2 \sqrt{21 x \cdot x \sqrt{14}}$

Combine exponents.

Raise $x$ to the power of $1$ .

$2 \sqrt{21 (x^{1} x) \sqrt{14}}$

Raise $x$ to the power of $1$ .

$2 \sqrt{21 (x^{1} x^{1}) \sqrt{14}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 \sqrt{21 x^{1 + 1} \sqrt{14}}$

Add $1$ and $1$ .

$2 \sqrt{21 x^{2} \sqrt{14}}$

Rewrite $21 x^{2} \sqrt{14}$ as $x^{2} \cdot (21 \sqrt{14})$ .

Reorder $21$ and $x^{2}$ .

$2 \sqrt{x^{2} \cdot 21 \sqrt{14}}$

Add parentheses.

$2 \sqrt{x^{2} \cdot (21 \sqrt{14})}$

Pull terms out from under the radical.

$2 x \sqrt{21 \sqrt{14}}$