Question

Find the greatest 4 digit number which is a perfect square.
(A) 9801
(B) 9999
(C) 1000
(D) 9898

Answer 1

Hint- First of all, we will find the smallest five digit number which will be a perfect square. After finding, we will subtract 1 from the square root of the smallest five digit perfect square number and square it to get the greatest 4 digit perfect square number.
Complete step-by-step solution -
The largest 4 digit number is 9999 which is not a perfect square.
Let us consider a five digit minimum number. It is 10000. It is a perfect square of 100 as
$ \Rightarrow 100*100 = 10000$
Now, the smallest five digit number is a perfect square of 100, the biggest 4 digit number which should be a perfect square will be one less than 100

$ = (99)*(99)$
$ = 9801$
Which is the same as option A.
So, A is the correct option.
Note- It can also be done by taking the square root of the greatest 4 digit number 9999 which comes out to be 99.99. By taking the next lower integer that is 99 and multiplying it by itself gives 9801. Also, the square of any 3 digit number will have either 5 or 6 digits. So, the largest 4 digit perfect square will be the square of largest two digit number that is 99.Thus 99*99=9801.