# Dear Sir/Madam,Thanks for your answer to my below question, but I could not understant, how will i deceide for Question A :- that will start from 45 2 =2025 < 2361 and for Question B:- is star5ting from  125 2 =15625Is there any trick?Thanks,DurgaPrasad Tripathy Dear  Madam/Sir, I was refering R.D Sharma textbook where in Exe- 3.5  Q.no. 2 to find least no. which must be subtracted from the following no.to make them perfect square   a. 2361    b. 16160     Could you please explain me the above question.   Thanking you, Divya Tripathy Ans: a. 45 2 =2025 < 2361 46 2 =2116 < 2361 47 2 =2209 <2361 48 2 =2304 < 2361 49 2 =2401 > 2361 So we observe, 48 2  < 2361 < 49 2 2304 < 2361 < 2401  Hence, the minumum nunber that needs to be subtracted to make it a perfect square is 2361 - 2304 = 57   b. 125 2 =15625 < 16160 126 2 =15876 < 16160 127 2 =16129 < 16160 128 2 =16384 > 16160 So we observe, 127 2  < 16160 < 128 2 16129 < 16160 < 16384 Hence, the minumum nunber that needs to be subtracted to make it a perfect square is 16160 - 16129 = 31

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