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.