Simplify the Radical Expression 5x square root of 12x^5

$5 x \sqrt{12 x^{5}}$

Rewrite $12 x^{5}$ as ${(2 x^{2})}^{2} \cdot (3 x)$ .

Factor $4$ out of $12$ .

$5 x \sqrt{4 (3) x^{5}}$

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

$5 x \sqrt{2^{2} \cdot 3 x^{5}}$

Factor out $x^{4}$ .

$5 x \sqrt{2^{2} \cdot 3 (x^{4} x)}$

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

$5 x \sqrt{2^{2} \cdot 3 ({(x^{2})}^{2} x)}$

Move $3$ .

$5 x \sqrt{2^{2} {(x^{2})}^{2} \cdot 3 x}$

Rewrite $2^{2} {(x^{2})}^{2}$ as ${(2 x^{2})}^{2}$ .

$5 x \sqrt{{(2 x^{2})}^{2} \cdot 3 x}$

Add parentheses.

$5 x \sqrt{{(2 x^{2})}^{2} \cdot (3 x)}$

Pull terms out from under the radical.

$5 x (| 2 x^{2} | \sqrt{3 x})$

Remove non-negative terms from the absolute value.

$5 x (2 x^{2} \sqrt{3 x})$

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

Move $x^{2}$ .

$5 (x^{2} x) (2 \sqrt{3 x})$

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

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

$5 (x^{2} x^{1}) (2 \sqrt{3 x})$

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

$5 x^{2 + 1} (2 \sqrt{3 x})$

Add $2$ and $1$ .

$5 x^{3} (2 \sqrt{3 x})$

Multiply $2$ by $5$ .

$10 x^{3} \sqrt{3 x}$