2. The square root of a two-digit number is expressed as an infinite decimal fraction, the first four digits of which (including the integer part) are the same. Find this number without using tables.
2. Let the desired number be $N_{\bullet}$ Then $10 \leqslant N \leqslant 100$. Therefore, $3, \ldots \leqslant$ $10,89$, i.e., $N=11 ; 12 ; \ldots$

But $\sqrt{11}=3.31662$. Therefore, there does not exist a two-digit number, the first four digits of the square root of which are written only with threes. By performing similar trials, we find that the desired number is 79, the square root of which is $8.888 \ldots$