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Example 11 Find the greatest 4-digit number which is a perfect square. Greatest 4-digit number = Finding Square root of 9999 by Long Division Here, Remainder = 198 Since remainder is not 0, So, 9999 is not a perfect square We need to find the greatest 4-digit number which is a perfect square So, we need to find a number smaller than 9999, as numbers bigger than 9999 are 5 digit numbers Thus, we subtract 198 (remainder) from 9999 to get a perfect square. ∴ Perfect square = 9999 − 198 Perfect square = 9801 Thus, 9801 is the required number

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.