The square of a number that ends in 5

How to calculate the square of a number that ends in 5 fast?

15*15=225
25*25=625
35*35=1225
45*45=2025
55*55=3025

We just delete the last digit of the number (the 5) and multiply this shorter number with the one that is bigger with 1 than it. After that we glue a 25 at the end of the product.

35*35=?
We delete the last digit and we have only 3.
The number added with 1 is 3+1=4.
The product is 3*4=12.
We glue a 25 in the end: 1225
35*35=1225

25*25=?
We delete de last digit and have only 2.
The number added with 1 is 2+1=3.
The product is 2*3=6.
We glue a 25 in the end: 625
25*25=625

Tests:
45*45=?
65*65=?
85*85=?
95*95=?

How does it work?

(a*10+5)*(a*10+5)=100*a*a+2*5*10*a+25=
=100*a*a+100*a+25=100*a*(a+1)+25

100*a*(a+1)+25 is exactly the number a multiplied by a+1 with a 25 glued at the end.

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