Recall the product rule for square roots: \(\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}\). This means you can multiply the expressions inside the square roots together under a single square root.
Identify the expressions inside each square root: the first is \$5x\( and the second is \)7y$.
Multiply the expressions inside the square roots: \(5x \times 7y = 35xy\).
Rewrite the product of the square roots as a single square root containing the product: \(\sqrt{5x} \cdot \sqrt{7y} = \sqrt{35xy}\).
This expression \(\sqrt{35xy}\) is the simplified product using the product rule for square roots.