Simplify square root of 2x^2* square root of 50x^3

$\sqrt{2 x^{2}} \cdot \sqrt{50 x^{3}}$

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

$\sqrt{x^{2} \cdot 2} \cdot \sqrt{50 x^{3}}$

Pull terms out from under the radical.

$x \sqrt{2} \cdot \sqrt{50 x^{3}}$

Rewrite $50 x^{3}$ as ${(5 x)}^{2} \cdot (2 x)$ .

Factor $25$ out of $50$ .

$x \sqrt{2} \cdot \sqrt{25 (2) x^{3}}$

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

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

Factor out $x^{2}$ .

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

Move $2$ .

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

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

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

Add parentheses.

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

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

Pull terms out from under the radical.

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

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

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

Multiply $x$ by $x$ .

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

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

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

Combine using the product rule for radicals.

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

Multiply $2$ by $2$ .

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

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

Simplify the expression.

Rewrite using the commutative property of multiplication.

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

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

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

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

Pull terms out from under the radical.

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

Multiply $2$ by $5$ .

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

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