How can an irrational number be finite?

Hi, I'm an IB student from Mexico and I'm dying to solve something.

As part of a homework i must fin the exact value of an irrational number (our teacher told us it would be a trinomial) but as far as I'm concerned an irrational number can't be exact.

The number is:

[IMG]file:///C:/Users/ANAMAR%7E1/AppData/Local/Temp/moz-screenshot-2.png[/IMG]The root of: the root of 1 plus the the root of 1 and so on...

I wasn't able to type it here bit it looks as if the first root is "housing" the next one and so on.

Thanks for you help and I really hope someone knows how to solve this! :)