Answer:
Yes, the simplified form of the given radical expression is rational.
Step-by-step explanation:
We are asked to determine whether the simplified form of \(2\sqrt{3} \cdot \sqrt{12}\) is rational or not.
To solve our given problem we will use exponent property for radicals \(a\sqrt{m}\cdot\sqrt{n}=a\sqrt{m\cdot n}\).
\(2\sqrt{3} \cdot \sqrt{12}=2\sqrt{3\cdot 12}\)
\(2\sqrt{3} \cdot \sqrt{12}=2\sqrt{36}\)
\(2\sqrt{3} \cdot \sqrt{12}=2*6\)
\(2\sqrt{3} \cdot \sqrt{12}=12\)
Since our given radical expression simplifies to a rational, therefore, our answer is yes.
