## Answer :

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

12.89 can be expressed as: [tex] \frac{1289}{100} [/tex]

[tex] \frac{12}{144}= \frac{1}{12} [/tex]

The above numbers can be expressed as a fraction, then the logical answer is: [tex] \sqrt{12} [/tex]

But we will check the answer:

[tex] \sqrt{12}= \sqrt{2^{2}*3 } =2* \sqrt{3} =3.4641016...[/tex]

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