easy finding square numbers ending in 5

We will see a method that allows us to find in an easy way the squares of numbers ending in 5, without ofcourse any calculator usage.


What is the square of 5 ?   $5^2=5*5=25$ ...that was easy

What is the square of 15 ? ...

This is a bit more difficult. We don't want to do the multiplication, so let's try something different.

We are seaking for the outcome of $15*15$

FACT: the number that we are looking for ends in 25.
Take the first digit of the number that you have to multiply (the 1 in our example) and multiply it with is's next integer.
getting: $1*2=2$. In what we find we write at the very end the 25, so we come up with 225
(i can imagine that you have already done it with the calculator)

Same logic we follow to find the outcome of  $25^2$
$2*3=6$, put at the end the 25 and you get the number 625.

The squares of  35,45,55,65,75,85,95 can be found with the same way and you can do it for practice.

The method is almost the same for a 3-digit number. For example, let's find the square of 325.
Leave at it's own loneliness the 5 and take the first two digits, meaning the 32.

$32*33=1056$, put at the end the 25 and you come up with: 105625

If the number has four digits, put aside the last 5 and multiply the 3-digit number that remains with it's next integer. At the outcome write 25 at the very end and you are done! Do the same for more digits.