Simplify square root of 30x^2* square root of 3x^2

$\sqrt{30 x^{2}} \cdot \sqrt{3 x^{2}}$

Reorder $30$ and $x^{2}$ .

$\sqrt{x^{2} \cdot 30} \cdot \sqrt{3 x^{2}}$

Pull terms out from under the radical.

$x \sqrt{30} \cdot \sqrt{3 x^{2}}$

Reorder $3$ and $x^{2}$ .

$x \sqrt{30} \cdot \sqrt{x^{2} \cdot 3}$

Pull terms out from under the radical.

$x \sqrt{30} \cdot (x \sqrt{3})$

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

Move $x$ .

$x \cdot x \sqrt{30} \cdot \sqrt{3}$

Multiply $x$ by $x$ .

$x^{2} \sqrt{30} \cdot \sqrt{3}$

$x^{2} \sqrt{30} \cdot \sqrt{3}$

Multiply $x^{2} \sqrt{30} \sqrt{3}$ .

Combine using the product rule for radicals.

$x^{2} \sqrt{3 \cdot 30}$

Multiply $3$ by $30$ .

$x^{2} \sqrt{90}$

$x^{2} \sqrt{90}$

Rewrite $90$ as $3^{2} \cdot 10$ .

Factor $9$ out of $90$ .

$x^{2} \sqrt{9 (10)}$

Rewrite $9$ as $3^{2}$ .

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

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

Pull terms out from under the radical.

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

Move $3$ to the left of $x^{2}$ .

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

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