1156 is a perfect square. Its prime factorisation is 2² × 17². All factors are in pairs. But 2800 = 2⁵ × 5² × 7, which has unpaired 2s and a 7, so 2800 is not a perfect square.
Class 8 Mathematics Ganita Prakash Chapter 1 A Square and A Cube NCERT solutions
Class 8 Mathematics Chapter 1 A Square and A Cube question answer
1156 is a perfect square because its prime factorisation is 2² × 17². All prime factors appear in pairs, so it equals (2 × 17)² = 34². On the other hand, 2800 = 2⁵ × 5² × 7. The factor 2 appears five times and 7 is unpaired, so we cannot group all the factors into pairs. Hence, 2800 is not a perfect square, while 1156 is.
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