Simplify square root of 5x^2* square root of 20x

$\sqrt{5 x^{2}} \cdot \sqrt{20 x}$

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

$\sqrt{x^{2} \cdot 5} \cdot \sqrt{20 x}$

Pull terms out from under the radical.

$x \sqrt{5} \cdot \sqrt{20 x}$

Rewrite $20 x$ as $2^{2} \cdot (5 x)$ .

Factor $4$ out of $20$ .

$x \sqrt{5} \cdot \sqrt{4 (5) x}$

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

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

Add parentheses.

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

Pull terms out from under the radical.

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

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

Combine using the product rule for radicals.

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

Multiply $5$ by $5$ .

$x (2 \sqrt{25 x})$

Simplify the expression.

Rewrite using the commutative property of multiplication.

$2 x \sqrt{25 x}$

Rewrite $25$ as $5^{2}$ .

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

Pull terms out from under the radical.

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

Multiply $5$ by $2$ .

$10 x \sqrt{x}$