To solve [tex]\(\sqrt{3} \cdot \sqrt{5} \cdot \sqrt{6}\)[/tex] and find its equivalent expression, let's break down the problem step by step.
1. Combine the square roots under a single radical:
Using the property of square roots [tex]\(\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}\)[/tex], we can combine the given radicals:
[tex]\[
\sqrt{3} \cdot \sqrt{5} \cdot \sqrt{6} = \sqrt{3 \cdot 5 \cdot 6}
\][/tex]
2. Perform the multiplications inside the radical:
Calculate the product inside the square root:
[tex]\[
3 \cdot 5 = 15
\][/tex]
[tex]\[
15 \cdot 6 = 90
\][/tex]
So, we have:
[tex]\[
\sqrt{3} \cdot \sqrt{5} \cdot \sqrt{6} = \sqrt{90}
\][/tex]
3. Simplify the square root:
To further simplify [tex]\(\sqrt{90}\)[/tex], let’s factorize 90 into its prime factors:
[tex]\[
90 = 9 \cdot 10 = (3^2) \cdot 10
\][/tex]
We can use the property [tex]\(\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}\)[/tex]:
[tex]\[
\sqrt{90} = \sqrt{(3^2) \cdot 10} = \sqrt{3^2} \cdot \sqrt{10} = 3 \cdot \sqrt{10}
\][/tex]
4. Match the equivalent expression:
Therefore, [tex]\(\sqrt{3} \cdot \sqrt{5} \cdot \sqrt{6} = 3 \sqrt{10}\)[/tex].
Hence, the correct choice is:
A. [tex]\(3 \sqrt{10}\)[/tex]
