Question

Is the simplified form of
`2 √(3) * √(12)`rational?

Answer 1

Given the expression :

`2√(3)*√(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