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Let x² be the largest six-digit perfect square. 

The largest six-digit number is 999,999, so 
x² ≤ 999,999. 

You know that 1,000² = 1,000,000, which is only 1 more than 999,999, so x² must be the next smaller square, which is (1,000 - 1)². 
(1,000 - 1)² = 999² = 998,001. 
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We know the greatest number of 6 digits is 999999.
 Then solving through division method,
We get quotient as 999.99 So it is not a perfect square.
But if we consider it to be as (1000-1)² which will be equal to 999².

             (1000 - 1)² = 999² = 998001
.·.The greatest 6 digit number which is a perfect square is 998001.        

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