# 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

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