This is another trick that my family already knew, but I only learnt it recently so I’m sharing it for anybody out there who doesn’t already know.

Squaring 2 digit numbers is easy if they end in 5.

5×5 = 25, so the last 2 digits of the answer will always be 25.

To find the first digits of the answer, take the first digit of the number you are squaring and multiply it by the next ten up.

Eg 65 x 65

The first digit is 6. The next ten up is 7, so to find the first digits of the answer you multiply 6×7.

6×7 = 42

The last two digits will always be 25 so 65^{2 }= 4225

35^{2} = 1225 (3×4 = 12 and the last 2 digits are 25)

85^{2} – 7225 (8×9 = 72 and the last 2 digits are 25)

It’s especially useful for squaring something-and-a-half eg 7.5 x 7.5. 7 x 8 = 56. The last two digits will be 2 and 5, but here you are using ½ not a whole number, so it won’t be 25 but .25 so the answer is 56.25. 3.5^{2} is 12.25 and so on.

If you enjoyed this trick, you might also enjoy this post on how to multiply 2 digit numbers by 11 in your head.