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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.