Simplify square root of 5x* square root of 10y

$\sqrt{5 x} \cdot \sqrt{10 y}$

Step 1

Multiply $\sqrt{5 x} \sqrt{10 y}$ .

Combine using the product rule for radicals.

$\sqrt{5 x (10 y)}$

Multiply $10$ by $5$ .

$\sqrt{50 x y}$

$\sqrt{50 x y}$

Step 2

Rewrite $50 x y$ as $5^{2} \cdot (2 x y)$ .

Factor $25$ out of $50$ .

$\sqrt{25 (2) x y}$

Rewrite $25$ as $5^{2}$ .

$\sqrt{5^{2} \cdot 2 x y}$

Add parentheses.

$\sqrt{5^{2} \cdot 2 (x y)}$

Add parentheses.

$\sqrt{5^{2} \cdot (2 x y)}$

$\sqrt{5^{2} \cdot (2 x y)}$

Step 3

Pull terms out from under the radical.

$5 \sqrt{2 x y}$

Related Questions