Question

1. use the product property to multiply. assume all variables can be any real number.

\sqrt{13x} \cdot \sqrt{39y}
\sqrt{13x} \cdot \sqrt{39y} = \underline{qquad}
(simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Step1: Recall Product Property of Radicals

The product property of radicals states that \(\sqrt{a}\cdot\sqrt{b}=\sqrt{ab}\) for non - negative real numbers \(a\) and \(b\). Here, we have \(\sqrt{13x}\cdot\sqrt{3y}\), so we can apply this property.
\(\sqrt{13x}\cdot\sqrt{3y}=\sqrt{(13x)\cdot(3y)}\)

Step2: Simplify the Product Inside the Radical

Multiply the coefficients and the variables inside the radical. \(13\times3 = 39\) and \(x\times y=xy\). So \(\sqrt{(13x)\cdot(3y)}=\sqrt{39xy}\)

Answer:

\(\sqrt{39xy}\)