Example 6. There are exactly 35 consecutive natural numbers whose integer parts of the arithmetic square roots are the same. Then, what is this identical integer?

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Analyzing to determine the integer part of a real number $a$ actually means finding two adjacent integers $n$ and $n+1$, such that $n \leqslant a < n+1$, at this point the integer part of $a$ is $n$. Using the property $2^{\circ}$ above, the answer to this question is 17.