To find which choice is equivalent to the product [tex]\(\sqrt{8} \cdot \sqrt{5}\)[/tex], we need to simplify this expression step by step.
First, recall the properties of square roots:
[tex]\[
\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}
\][/tex]
Using this property, we can combine the square roots:
[tex]\[
\sqrt{8} \cdot \sqrt{5} = \sqrt{8 \cdot 5}
\][/tex]
Next, we calculate the product inside the square root:
[tex]\[
8 \cdot 5 = 40
\][/tex]
So, we have:
[tex]\[
\sqrt{8} \cdot \sqrt{5} = \sqrt{40}
\][/tex]
Now, we need to simplify [tex]\(\sqrt{40}\)[/tex]. We can factor 40 into a product of a perfect square and another number:
[tex]\[
40 = 4 \cdot 10
\][/tex]
Therefore,
[tex]\[
\sqrt{40} = \sqrt{4 \cdot 10} = \sqrt{4} \cdot \sqrt{10}
\][/tex]
Since the square root of 4 is 2, we get:
[tex]\[
\sqrt{40} = 2 \cdot \sqrt{10}
\][/tex]
Thus, the simplified form of [tex]\(\sqrt{8} \cdot \sqrt{5}\)[/tex] is:
[tex]\[
\sqrt{8} \cdot \sqrt{5} = 2 \cdot \sqrt{10}
\][/tex]
Now we compare this result to the given choices:
A. [tex]\(10 \sqrt{2}\)[/tex]
B. [tex]\(\sqrt{13}\)[/tex]
C. [tex]\(4 \sqrt{10}\)[/tex]
D. [tex]\(2 \cdot \sqrt{10}\)[/tex]
The correct answer is:
D. [tex]\(2 \sqrt{10}\)[/tex]
