To determine the equivalent expression for the product [tex]\(\sqrt{7x} \cdot \sqrt{x+2}\)[/tex], we can make use of the property of square roots that states [tex]\(\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}\)[/tex].
1. Start with the given product:
[tex]\[
\sqrt{7x} \cdot \sqrt{x+2}
\][/tex]
2. Apply the property of square roots to combine the two square roots into one:
[tex]\[
\sqrt{7x} \cdot \sqrt{x+2} = \sqrt{(7x) \cdot (x+2)}
\][/tex]
3. Distribute [tex]\(7x\)[/tex] inside the square root:
[tex]\[
\sqrt{7x \cdot (x+2)} = \sqrt{7x \cdot x + 7x \cdot 2} = \sqrt{7x^2 + 14x}
\][/tex]
Thus, the expression [tex]\(\sqrt{7x} \cdot \sqrt{x+2}\)[/tex] is equivalent to [tex]\(\sqrt{7x^2 + 14x}\)[/tex].
Among the given choices, the correct answer is:
A. [tex]\(\sqrt{7 x^2 + 14 x}\)[/tex]
