To determine which choice is equivalent to the product [tex]\(\sqrt{8} \cdot \sqrt{5}\)[/tex], we can follow these steps:
1. Simplify the Product of Square Roots:
The expression [tex]\(\sqrt{8} \cdot \sqrt{5}\)[/tex] can be combined into a single square root using the property of square roots: [tex]\(\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}\)[/tex].
[tex]\[
\sqrt{8} \cdot \sqrt{5} = \sqrt{8 \cdot 5}
\][/tex]
2. Calculate the Combined Radicand:
Multiply the numbers inside the square root:
[tex]\[
8 \cdot 5 = 40
\][/tex]
So, the expression becomes:
[tex]\[
\sqrt{8} \cdot \sqrt{5} = \sqrt{40}
\][/tex]
3. Simplify the Square Root:
Next, we simplify [tex]\(\sqrt{40}\)[/tex]. To do this, we look for perfect square factors of 40.
[tex]\[
40 = 4 \times 10
\][/tex]
Notice that 4 is a perfect square ([tex]\(4 = 2^2\)[/tex]). Hence:
[tex]\[
\sqrt{40} = \sqrt{4 \times 10} = \sqrt{4} \times \sqrt{10} = 2 \times \sqrt{10}
\][/tex]
Therefore, the simplified form of [tex]\(\sqrt{40}\)[/tex] is [tex]\(2 \sqrt{10}\)[/tex].
4. Compare with Given Choices:
We now compare our simplified result [tex]\(2 \sqrt{10}\)[/tex] with the given choices:
[tex]\[
\text{A. } 10 \sqrt{2}
\][/tex]
[tex]\[
\text{B. } 4 \sqrt{10}
\][/tex]
[tex]\[
\text{C. } 2 \sqrt{10}
\][/tex]
[tex]\[
\text{D. } \sqrt{13}
\][/tex]
The expression [tex]\(2 \sqrt{10}\)[/tex] matches exactly with choice C.
Thus, the correct answer is:
[tex]\[
\boxed{2 \sqrt{10}}
\][/tex]
