Let's start by rewriting the given expression in a simpler form:
[tex]\[
\sqrt{2} \cdot \sqrt{10} \cdot \sqrt{5}
\][/tex]
Using the property of square roots that [tex]\(\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}\)[/tex], we can combine the square roots:
[tex]\[
\sqrt{2} \cdot \sqrt{10} \cdot \sqrt{5} = \sqrt{2 \cdot 10 \cdot 5}
\][/tex]
Now let's multiply the numbers inside the square root:
[tex]\[
2 \cdot 10 \cdot 5 = 100
\][/tex]
So, we have:
[tex]\[
\sqrt{2 \cdot 10 \cdot 5} = \sqrt{100}
\][/tex]
The square root of 100 is:
[tex]\[
\sqrt{100} = 10
\][/tex]
Therefore, the product [tex]\(\sqrt{2} \cdot \sqrt{10} \cdot \sqrt{5}\)[/tex] simplifies to 10.
Among the given choices:
A. [tex]\(2 \sqrt{50}\)[/tex]
B. 10
C. [tex]\(4 \sqrt{25}\)[/tex]
D. [tex]\(5 \sqrt{2}\)[/tex]
The correct choice is B:
[tex]\[
10
\][/tex]
