Simplify 2 square root of x5 square root of 6x square root of 2x

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

Multiply $2 \sqrt{x} (5 \sqrt{6 x})$ .

Multiply $5$ by $2$ .

$10 \sqrt{x} \sqrt{6 x} \cdot \sqrt{2 x}$

Combine using the product rule for radicals.

$10 \sqrt{6 x \cdot x} \cdot \sqrt{2 x}$

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

$10 \sqrt{6 (x^{1} x)} \cdot \sqrt{2 x}$

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

$10 \sqrt{6 (x^{1} x^{1})} \cdot \sqrt{2 x}$

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

$10 \sqrt{6 x^{1 + 1}} \cdot \sqrt{2 x}$

Add $1$ and $1$ .

$10 \sqrt{6 x^{2}} \cdot \sqrt{2 x}$

Reorder $6$ and $x^{2}$ .

$10 \sqrt{x^{2} \cdot 6} \cdot \sqrt{2 x}$

Pull terms out from under the radical.

$10 (x \sqrt{6}) \cdot \sqrt{2 x}$

Multiply $10 x \sqrt{6} \sqrt{2 x}$ .

Combine using the product rule for radicals.

$10 x \sqrt{2 x \cdot 6}$

Multiply $6$ by $2$ .

$10 x \sqrt{12 x}$

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

Factor $4$ out of $12$ .

$10 x \sqrt{4 (3) x}$

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

$10 x \sqrt{2^{2} \cdot 3 x}$

Add parentheses.

$10 x \sqrt{2^{2} \cdot (3 x)}$

Pull terms out from under the radical.

$10 x (2 \sqrt{3 x})$

Multiply $2$ by $10$ .

$20 x \sqrt{3 x}$

Simplify 2 square root of x*5 square root of 6x* square root of 2x