## 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.