Simplify square root of 3x* square root of 81x

$\sqrt{3 x} \cdot \sqrt{81 x}$

Step 1

Rewrite $81 x$ as ${(3^{2})}^{2} x$ .

Rewrite $81$ as $9^{2}$ .

$\sqrt{3 x} \cdot \sqrt{9^{2} x}$

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

Simplify the expression.

Rewrite using the commutative property of multiplication.

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

Raise $3$ to the power of $2$ .

$9 \sqrt{3 x} \sqrt{x}$

Step 4

Multiply $9 \sqrt{3 x} \sqrt{x}$ .

Combine using the product rule for radicals.

$9 \sqrt{x (3 x)}$

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

$9 \sqrt{3 (x^{1} x)}$

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

$9 \sqrt{3 (x^{1} x^{1})}$

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

$9 \sqrt{3 x^{1 + 1}}$

Add $1$ and $1$ .

$9 \sqrt{3 x^{2}}$

Step 5

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

$9 \sqrt{x^{2} \cdot 3}$

Step 6

Pull terms out from under the radical.

$9 x \sqrt{3}$