Simplify square root of 3x^2* square root of 4x

$\sqrt{3 x^{2}} \cdot \sqrt{4 x}$

Step 1

Reorder $3$ and $x^{2}$ .

$\sqrt{x^{2} \cdot 3} \cdot \sqrt{4 x}$

Step 2

Pull terms out from under the radical.

$x \sqrt{3} \cdot \sqrt{4 x}$

Step 3

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

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

Step 4

Pull terms out from under the radical.

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

Step 5

Combine using the product rule for radicals.

$x (2 \sqrt{3 x})$

Step 6

Rewrite using the commutative property of multiplication.

$2 x \sqrt{3 x}$