Simplify square root of 3x* square root of 5x

$\sqrt{3 x} \cdot \sqrt{5 x}$

Step 1

Multiply $\sqrt{3 x} \sqrt{5 x}$ .

Combine using the product rule for radicals.

$\sqrt{3 x (5 x)}$

Multiply $5$ by $3$ .

$\sqrt{15 x \cdot x}$

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

$\sqrt{15 (x^{1} x)}$

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

$\sqrt{15 (x^{1} x^{1})}$

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

$\sqrt{15 x^{1 + 1}}$

Add $1$ and $1$ .

$\sqrt{15 x^{2}}$

Step 2

Reorder $15$ and $x^{2}$ .

$\sqrt{x^{2} \cdot 15}$

Step 3

Pull terms out from under the radical.

$x \sqrt{15}$