# 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

**45 2 =2025 < 2361**

**125 2 =15625**

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

### Asked by divya.tripathy | 25th Jun, 2015, 11:40: AM

Expert Answer:

### 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 40^{2}=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. 45^{2}=2025 which is less than 2361.
Similarly for part (b), we could have started from 120^{2}. 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 "**N**5". We find N(N+1) and we simply place 25 to the right of that number.
For example to find square of **4**5, we find 4(4+1)=4*5=**20**, and we place 25 to the right of it. So the number becomes **20**25. Hence, 45^{2}=2025.
To find the square of **12**5, we find 12(12+1)=12*13=**156**, and we place 25 to the right of it. So the number becomes **156**25. Hence, 125^{2}=15625.

^{2}=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.

^{2}=2025 which is less than 2361.

^{2}. But since 125 ends in 5 and its square can be found easily, we started from 125.

**N**5". We find N(N+1) and we simply place 25 to the right of that number.

**4**5, we find 4(4+1)=4*5=

**20**, and we place 25 to the right of it. So the number becomes

**20**25. Hence, 45

^{2}=2025.

**12**5, we find 12(12+1)=12*13=

**156**, and we place 25 to the right of it. So the number becomes

**156**25. Hence, 125

^{2}=15625.

### Answered by satyajit samal | 26th Jun, 2015, 09:46: AM

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