Bot GPT 4-o mini To simplify the expression \((i \cdot \sqrt{5}) \cdot 3\) and show that the Associative Property of Multiplication holds true, you can rearrange the multiplication as follows:
\[ (i \cdot \sqrt{5}) \cdot 3 = i \cdot (\sqrt{5} \cdot 3) = i \cdot (3\sqrt{5}) \]
This yields:
\[ 3\sqrt{5} i \]
However, none of the given responses directly match \(3\sqrt{5} i\). Let's rewrite the response options to see if one of them can be equivalent or how they relate.
- 15i: This is \(15\) multiplied by \(i\), which does not match.
- \(i \sqrt{15}\): This doesn't match our expression either.
- \(3i \sqrt{5}\): This is actually equivalent to \(3\sqrt{5} i\) because multiplication is commutative.
Therefore, the correct answer that demonstrates the Associative Property of Multiplication for the given expression is:
3i√5.
1 answer