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The greatest 6-digit no is 999999
Now finding the square root of 999999
we get,

Now since we need a perfect square 
We find the square of the no 999 without considering the decimal places,

So now we have,

So, the greatest 6-digit number which is a perfect square is 998001.
The smallest 6 digit number is 100000
 We find the square root of 100000 : = 316.227766 We take the next larger whole number 317,  We square 317
  317² =
100489 That's the smallest perfect square which is a 6-digit number, because when we square 316 we only get 99856, which is only a 5-digit number.