If $N^2 = 12345678987654321$, then how many digits does the number N have?

If $N^2 = 12345678987654321$, then how many digits does the number N have?
  1. 8
  2. 9
  3. 10
  4. 11

Solution

The number 12345678987654321 is the well-known square of the repunit $111111111$ (nine 1s). That is, $(111111111)^2 = 12345678987654321$. Hence $N = 111111111$, which has 9 digits.

Asked in: CSAT 2025

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