Verified Answer :

Good night, 

Irrational numbers
are those that can't be expressed as a fraction:

12.89 can be expressed as: 
\(\frac{1289}{100}\)

\(\frac{12}{144}= \frac{1}{12}\)

The above numbers
can be expressed as a fraction, then the logical answer is: 
\(\sqrt{12}\)

But we will check the answer: 

\(\sqrt{12}= \sqrt{2^{2}*3 } =2* \sqrt{3} =3.4641016...\)

As you can see we can't express that number as a fraction, so that is te correct answer.