Simplify square root of 6x square root of 9x

$\sqrt{6 x} \sqrt{9 x}$

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

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

Pull terms out from under the radical.

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

Rewrite using the commutative property of multiplication.

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

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

Combine using the product rule for radicals.

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

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

$3 \sqrt{6 (x^{1} x)}$

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

$3 \sqrt{6 (x^{1} x^{1})}$

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

$3 \sqrt{6 x^{1 + 1}}$

Add $1$ and $1$ .

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

Reorder $6$ and $x^{2}$ .

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

Pull terms out from under the radical.

$3 x \sqrt{6}$