Simplify square root of 10x* square root of 2x

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

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

Combine using the product rule for radicals.

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

Multiply $2$ by $10$ .

$\sqrt{20 x \cdot x}$

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

$\sqrt{20 (x^{1} x)}$

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

$\sqrt{20 (x^{1} x^{1})}$

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

$\sqrt{20 x^{1 + 1}}$

Add $1$ and $1$ .

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

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

Factor $4$ out of $20$ .

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

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

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

Move $5$ .

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

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

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

Pull terms out from under the radical.

$2 x \sqrt{5}$