Given:25x25 How to evaluate the square of double figures whose ones digit is limited to 5 like this problem is shown below:
First, just write down the product of (its tens digit,2) times (the sum of tens digit and 1, 3=2+1). That is: 2x(2+1)=2x3=6. 6 is the product to write down first.
Then, write down 25(=5x5) anytime to the right of 6: 6 then 25. That is 625. We have: 25x25=625.
In the same manner, 15x15 : 2(=1x2) then 25. That is: 225 We have: 15x15=225.
35x35: 12(=3x4) then 25. That is: 1225 we have: 35x35=1225.
45x45=2025, 55x55=3025, 65x65=4225, 75x75=5625, 85x85=7225, and 95x95=9025*
The answer is: 25x25=625
* This is just for convenience, so proving is skipped, but can be proved using (a+b)²=a²+2ab+b².
(10a+5)²=100a²+100a+25=a(a+1)x100+25