find the greatest number of 6 digit which is a perfect square find the square root of this number
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998001 is the no... it is square of 999
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The greatest 6-digit number is 999 999. Since it isn't a perfect square, it follows that the greatest 6-digit number which is one (let's call it G), can't be other than the square of the integer part of the square root of 999 999:
G = { integer [sqrt (999 999) ] }² . We have:
999 999 = 10⁶ - 1 = (10³ +1)(10³ - 1) = 1001 * 999
The next integer to 999 is 1000, whose square is 1 000 000 > 999 999, so 999 is the greatest 3-digit number with a 6-digit square. It follows that:
G = 999² = 998 001
The greatest 6-digit number is 999 999. Since it isn't a perfect square, it follows that the greatest 6-digit number which is one (let's call it G), can't be other than the square of the integer part of the square root of 999 999:
G = { integer [sqrt (999 999) ] }² . We have:
999 999 = 10⁶ - 1 = (10³ +1)(10³ - 1) = 1001 * 999
The next integer to 999 is 1000, whose square is 1 000 000 > 999 999, so 999 is the greatest 3-digit number with a 6-digit square. It follows that:
G = 999² = 998 001
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