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 =15625

 

Is 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   

For part (a), since the number given is 2361, we have to find a number whose square is less than 2361.

We could have started with 40 also. We know that 40²=1600. There is a huge gap between 1600 and 2361. So we can try for numbers more than 40, like 41, 42 and so on.

We can use the trick to quickly find the square of a number ending in 5. 45²=2025 which is less than 2361. 

Similarly for part (b), we could have started from 120². But since 125 ends in 5 and its square can be found easily, we started from 125. 

 

(Method to quickly find square of a number ending in 5. Let the number be "N5". We find N(N+1) and we simply place 25 to the right of that number. 

For example to find square of 45, we find 4(4+1)=4*5=20, and we place 25 to the right of it. So the number becomes 2025. Hence, 45²=2025.

To find the square of 125, we find 12(12+1)=12*13=156, and we place 25 to the right of it. So the number becomes 15625. Hence, 125²=15625.