To determine which choice is equivalent to the product [tex]\( \sqrt{3} \cdot \sqrt{5} \cdot \sqrt{6} \)[/tex], let's go through a step-by-step simplification process:
1. Combine the Square Roots Using Multiplication Property:
[tex]\[
\sqrt{3} \cdot \sqrt{5} \cdot \sqrt{6} = \sqrt{3 \times 5 \times 6}
\][/tex]
2. Multiply the Numbers Inside the Square Root:
[tex]\[
3 \times 5 \times 6 = 90
\][/tex]
3. Rewrite the Expression:
[tex]\[
\sqrt{3} \cdot \sqrt{5} \cdot \sqrt{6} = \sqrt{90}
\][/tex]
Now let's look at each of the answer choices and determine if any match the simplified form [tex]\( \sqrt{90} \)[/tex]:
A. [tex]\( 9 \sqrt{10} \)[/tex]
B. [tex]\( 3 \sqrt{5} \)[/tex]
C. [tex]\( 10 \sqrt{3} \)[/tex]
D. [tex]\( 3 \sqrt{10} \)[/tex]
First, we note that none of the expressions are in the form of a single square root of a number directly. However, we can use the decimal equivalence from our earlier steps to match exactly:
[tex]\[
\sqrt{90} \approx 9.4868
\][/tex]
Comparing this decimal result with the options, we see that
[tex]\[
9.4868 \approx 9.4868
\][/tex]
This matches our calculated value for [tex]\( \sqrt{90} \)[/tex].
Since [tex]\(\sqrt{90}\)[/tex] is exactly the value we have simplified, the correct equivalent expression matching the given product is indeed not directly among the options provided, but understanding the equivalence, we know none of the provided choices can be converted exactly to match [tex]\(\sqrt{90}\)[/tex].
However, in mathematical equivalency only considering a decimal match, we find the conclusion that none of the provided options directly simplify to the equivalent expression of [tex]\( \sqrt{90} \)[/tex], suggesting a reformulation of provided multiple choices is required to include [tex]\( \sqrt{90} \)[/tex].
