Let's find the equivalent expression for the product [tex]\(\sqrt{14} \cdot \sqrt{10}\)[/tex].
First, recall the property of square roots that states:
[tex]\[
\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}
\][/tex]
Applying this property, we have:
[tex]\[
\sqrt{14} \cdot \sqrt{10} = \sqrt{14 \cdot 10}
\][/tex]
Now, we simplify the expression inside the square root:
[tex]\[
14 \cdot 10 = 140
\][/tex]
Therefore:
[tex]\[
\sqrt{14} \cdot \sqrt{10} = \sqrt{140}
\][/tex]
To see if we can simplify [tex]\(\sqrt{140}\)[/tex] further, we factorize 140:
[tex]\[
140 = 2 \cdot 70 = 2 \cdot 2 \cdot 35 = 4 \cdot 35
\][/tex]
So, we can write:
[tex]\[
\sqrt{140} = \sqrt{4 \cdot 35}
\][/tex]
Using the property of square roots, [tex]\(\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}\)[/tex], we can separate this:
[tex]\[
\sqrt{140} = \sqrt{4 \cdot 35} = \sqrt{4} \cdot \sqrt{35}
\][/tex]
We know that:
[tex]\[
\sqrt{4} = 2
\][/tex]
Thus:
[tex]\[
\sqrt{140} = 2 \cdot \sqrt{35}
\][/tex]
Therefore, the equivalent expression for [tex]\(\sqrt{14} \cdot \sqrt{10}\)[/tex] is:
[tex]\[
2 \cdot \sqrt{35}
\][/tex]
Hence, the correct choice is:
B. [tex]\(2 \sqrt{35}\)[/tex]
