Question

Is the simplified form of $2 \sqrt{3} \times \sqrt{12}$rational?

Answer 1

Given the expression :

$2\sqrt{3}\times\sqrt{12}$

the answer will be as following :

$\begin{gathered} 12=2\cdot2\cdot3=2^2\cdot3 \\ \sqrt[]{12}=\sqrt[]{2^2\cdot3}=2\sqrt[]{3} \end{gathered}$

So,

$2\sqrt[]{3}\cdot\sqrt[]{12}=2\sqrt[]{3}\cdot2\sqrt[]{3}=2\cdot2\cdot\sqrt[]{3}\cdot\sqrt[]{3}=4\cdot3=12$

12 is a rational number