# Square of a number which lies between 41 and 49

Proof: Any number from 41 to 49 can be represented as (50 – a). Taking the square of this number we have equation as:
$$(50-a)^{2}$$ = $$50^{2}$$ - 2 $$\times$$ 50 $$\times$$ a + $$a^{2}$$ = 2500 - 100a + $$a^{2}$$ = 100(25-a) + $$a^{2}$$ = (25-a) / $$a^{2}$$

Steps for better understand:
Step 1: 46 is 4 less than 50. So a=4. Obtain the square of this digit.  Obtain the square of 4 to get 16. This forms the 2nd part of the answer.
Step 2: Subtract 4 from 25 to get 21. This forms the 1st part of the answer.
So, $$46^{2}$$ = 2116

One more Example: