Between which two consecutive integers does $\sqrt{75}$ lie?

Between which two consecutive integers does $\sqrt{75}$ lie?
  1. $8$ and $9$
  2. $7$ and $8$
  3. $9$ and $10$
  4. $6$ and $7$

Solution

$8^{2} = 64 < 75 < 81 = 9^{2}$, so $8 < \sqrt{75} < 9$.

Asked in: IMO

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