Simplify 4 square root of 6y*3 square root of 7x^2y

$4 \sqrt{6 y} \cdot 3 \sqrt{7 x^{2} y}$

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

Reorder $7$ and $x^{2}$ .

$4 \sqrt{6 y} \cdot (3 \sqrt{x^{2} \cdot 7 y})$

Add parentheses.

$4 \sqrt{6 y} \cdot (3 \sqrt{x^{2} \cdot (7 y)})$

Pull terms out from under the radical.

$4 \sqrt{6 y} \cdot (3 (x \sqrt{7 y}))$

Multiply $4 \sqrt{6 y} (3 x \sqrt{7 y})$ .

Multiply $3$ by $4$ .

$12 \sqrt{6 y} (x \sqrt{7 y})$

Combine using the product rule for radicals.

$12 (x \sqrt{6 y (7 y)})$

Multiply $7$ by $6$ .

$12 (x \sqrt{42 y \cdot y})$

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

$12 (x \sqrt{42 (y^{1} y)})$

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

$12 (x \sqrt{42 (y^{1} y^{1})})$

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

$12 (x \sqrt{42 y^{1 + 1}})$

Add $1$ and $1$ .

$12 (x \sqrt{42 y^{2}})$

Reorder $42$ and $y^{2}$ .

$12 (x \sqrt{y^{2} \cdot 42})$

Pull terms out from under the radical.

$12 (x (y \sqrt{42}))$

Rewrite using the commutative property of multiplication.

$12 \sqrt{42} x y$