Simplify 8x^3 square root of 12x+4x^2 square root of 3x^3

$8 x^{3} \sqrt{12 x} + 4 x^{2} \sqrt{3 x^{3}}$

Simplify each term.

Rewrite $12 x$ as $2^{2} \cdot (3 x)$ .

Factor $4$ out of $12$ .

$8 x^{3} \sqrt{4 (3) x} + 4 x^{2} \sqrt{3 x^{3}}$

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

$8 x^{3} \sqrt{2^{2} \cdot 3 x} + 4 x^{2} \sqrt{3 x^{3}}$

Add parentheses.

$8 x^{3} \sqrt{2^{2} \cdot (3 x)} + 4 x^{2} \sqrt{3 x^{3}}$

Pull terms out from under the radical.

$8 x^{3} (2 \sqrt{3 x}) + 4 x^{2} \sqrt{3 x^{3}}$

Multiply $2$ by $8$ .

$16 x^{3} \sqrt{3 x} + 4 x^{2} \sqrt{3 x^{3}}$

Rewrite $3 x^{3}$ as $x^{2} \cdot (3 x)$ .

Factor out $x^{2}$ .

$16 x^{3} \sqrt{3 x} + 4 x^{2} \sqrt{3 (x^{2} x)}$

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

$16 x^{3} \sqrt{3 x} + 4 x^{2} \sqrt{x^{2} \cdot 3 x}$

Add parentheses.

$16 x^{3} \sqrt{3 x} + 4 x^{2} \sqrt{x^{2} \cdot (3 x)}$

Pull terms out from under the radical.

$16 x^{3} \sqrt{3 x} + 4 x^{2} (x \sqrt{3 x})$

Multiply $x^{2}$ by $x$ by adding the exponents.

Move $x$ .

$16 x^{3} \sqrt{3 x} + 4 (x \cdot x^{2}) \sqrt{3 x}$

Multiply $x$ by $x^{2}$ .

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

$16 x^{3} \sqrt{3 x} + 4 (x^{1} x^{2}) \sqrt{3 x}$

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

$16 x^{3} \sqrt{3 x} + 4 x^{1 + 2} \sqrt{3 x}$

Add $1$ and $2$ .

$16 x^{3} \sqrt{3 x} + 4 x^{3} \sqrt{3 x}$

Add $16 x^{3} \sqrt{3 x}$ and $4 x^{3} \sqrt{3 x}$ .

$20 x^{3} \sqrt{3 x}$