Simplify square root of 5x^3* square root of 12x^6

$\sqrt{5 x^{3}} \cdot \sqrt{12 x^{6}}$

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

Factor out $x^{2}$ .

$\sqrt{5 (x^{2} x)} \cdot \sqrt{12 x^{6}}$

Reorder $5$ and $x^{2}$ .

$\sqrt{x^{2} \cdot 5 x} \cdot \sqrt{12 x^{6}}$

Add parentheses.

$\sqrt{x^{2} \cdot (5 x)} \cdot \sqrt{12 x^{6}}$

Pull terms out from under the radical.

$x \sqrt{5 x} \cdot \sqrt{12 x^{6}}$

Rewrite $12 x^{6}$ as ${(2 x^{3})}^{2} \cdot 3$ .

Factor $4$ out of $12$ .

$x \sqrt{5 x} \cdot \sqrt{4 (3) x^{6}}$

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

$x \sqrt{5 x} \cdot \sqrt{2^{2} \cdot 3 x^{6}}$

Rewrite $x^{6}$ as ${(x^{3})}^{2}$ .

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

Move $3$ .

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

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

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

Pull terms out from under the radical.

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

Rewrite using the commutative property of multiplication.

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

Multiply $x$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

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

Multiply $x^{3}$ by $x$ .

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

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

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

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

Add $3$ and $1$ .

$2 \sqrt{3} x^{4} \sqrt{5 x}$

Multiply $2 \sqrt{3} x^{4} \sqrt{5 x}$ .

Combine using the product rule for radicals.

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

Multiply $3$ by $5$ .

$2 x^{4} \sqrt{15 x}$