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$\sqrt {n}$ needs to be between $9$ and $11$
$\therefore n$ needs to be between $81$ and $121$
So $n= 82, 83, ... , 119, 120$
$\overbrace{\underbrace{1, 2, 3, ..., 80, 81}_{81\text{ numbers}}, 82, ..., 120}^{120\text{ numbers}}$
So $82, ..., 120$ is $120-81=39$ numbers.