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

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

Step 1

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

Combine using the product rule for radicals.

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

Multiply $6$ by $3$ .

$\sqrt{18 x \cdot x}$

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

$\sqrt{18 (x^{1} x)}$

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

$\sqrt{18 (x^{1} x^{1})}$

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

$\sqrt{18 x^{1 + 1}}$

Add $1$ and $1$ .

$\sqrt{18 x^{2}}$

Step 2

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

Factor $9$ out of $18$ .

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

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

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

Move $2$ .

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

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

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

Step 3

Pull terms out from under the radical.

$3 x \sqrt{2}$