Oh, dude, the closest square number to 9,999 is 100 squared, which is 10,000. I mean, it's like almost there but not quite, you know? So, yeah, 10,000 is the square number just chilling next to 9,999.
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The closest square number will be as close to 9999 as you like.
For example, 99.999 square = 9999.800001 (0.800001 away)
99.995 square = 9999.000025 (0.000025 away)
You could get closer still.
The nearest PERFECT square, however, is 10,000.
82 is not the square of an integer. The closest square number of an integer is 81, which is equal to 9 squared.
999 + 999/999
An infinite number of ways. 99+9/9 (99+9/9)*9/9 (99+9/9)*99/99 (99+9/9)*999/999 (99+9/9)*9/9*9/9 etc
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8,999,999,999,999,999,999,999,999,999,999,999,999,999,999,991 (8 quattuordecillion, 999 tredecillion, 999 duodecillion, 999 undecillion, 999 decillion, 999 nonillion, 999 octillion, 999 septillion, 999 sextillion, 999 quintillion, 999 quadrillion, 999 trillion, 999 billion, 999 million, 999 thousand and 991)