Simplify square root of 6x* square root of 3x^2

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Algebra

$\sqrt{6 x} \cdot \sqrt{3 x^{2}}$

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

$\sqrt{6 x} \cdot \sqrt{x^{2} \cdot 3}$

Pull terms out from under the radical.

$\sqrt{6 x} \cdot (x \sqrt{3})$

Rewrite using the commutative property of multiplication.

$\sqrt{3} \sqrt{6 x} x$

Multiply $\sqrt{3} \sqrt{6 x}$ .

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Combine using the product rule for radicals.

$\sqrt{3 (6 x)} x$

Multiply $3$ by $6$ .

$\sqrt{18 x} x$

Rewrite $18 x$ as $3^{2} \cdot (2 x)$ .

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Factor $9$ out of $18$ .

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

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

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

Add parentheses.

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

Pull terms out from under the radical.

$3 \sqrt{2 x} x$

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