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Problem #16 · August 12, 2026

Powers and roots

Between which two consecutive natural numbers does 75\sqrt{75} lie?
  1. A7 and 8
  2. B9 and 10
  3. C37 and 38
  4. D74 and 76
  5. E8 and 9

WORKED EXAMPLE

Solution

Compare the squares of consecutive natural numbers: 82=648^{2} = 64 and 92=819^{2} = 81. Since 64<75<8164 < 75 < 81, we have 8<75<98 < \sqrt{75} < 9.
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