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The answer is 99856 which is a square of +316 or -316.
99856= \sqrt{2 ^{4} *  79^{2} } =2²*79=316.
And , we see that 99856 is the closest required number to 99999 , which is the largest 5 digit no.
So the required number is 99856
Note:This can be done in 3 different methods:
1>Prime Factorization
2>Trial and Error
1 5 1
you should first try to find the square root of the "greatest five-digit number" which would be 316 point something. then you should find the square of 316 which will be the answer.
no one can just guess the number 99856 or 316 have to find it..
Yes it can be done easily in the division method but unfortunately , i can't show it here:(
99856 is the greatest five digit number which is a perfect square.