Question

Find the least number which must be subtracted from 2361 to get a perfect square

Answer 1

If you are not allowed to use a calculator then use following method:

The square root of 2361 would be something between 48 and 50.

Since we know that square of 50 is 2500

So, taking numbers less than 50.

Now, square of 49 is 2401, which is greater than 2361.

Square of 48, which is 2304, which is smaller than 2361.

So, 2361–2304= 57

And if you are allowed to use calculator then simply take square root of 2361, which is 48.59

Now take square of 48 and subtract it from 2361

i.e. 2361–2304 = 57