If N² = 12345678987654321, then how many digits does the number N have?

Answer: (b) 9

A perfect square with 17 digits has a square root of (17 + 1)/2 = 9 digits. Indeed 111111111² = 12345678987654321, and 111111111 has 9 digits.

1. 12345678987654321 has 17 digits.
2. A square with an odd number of digits d has a root with (d + 1)/2 digits: (17 + 1)/2 = 9.
3. Check: 111111111² = 12345678987654321, and 111111111 has 9 digits.

Remember · Digits in √N: (d + 1)/2 if N has d digits with d odd, d/2 if d is even. Also, 11…1² gives 12…n…21.

Question and answer: UPSC's official GS Paper II (2025, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). · Report an error