Squaring numbers that end in 5

Hello, and welcome to Myriora Maths! Thirty-five squared. In your head, in two seconds. Here's how!

Take the digit in front of the five: three. Multiply it by the next number up: three times four is twelve. Then put twenty-five on the end. One thousand, two hundred and twenty-five!

Let's try sixty-five squared. Six times seven is forty-two. Put twenty-five on the end: four thousand, two hundred and twenty-five. And one hundred and fifteen squared? Eleven times twelve is one hundred and thirty-two. So, thirteen thousand, two hundred and twenty-five!

Why does it work? Here's thirty-five squared, as a big square, thirty-five on each side. Cut off the strip down the right side, turn it, and put it at the bottom. Now we have a rectangle, thirty wide and forty tall. Plus a little five by five square, left over. Thirty times forty is twelve hundred. Plus twenty-five!

Careful! The trick only works when the last digit is five. Thirty-four squared is not three times four with sixteen on the end. That's too big. It's actually one thousand, one hundred and fifty-six.

Your turn! What is seventy-five squared? You've got twenty seconds, or pause the video if you need more time. Go!

Time's up! Seven times eight is fifty-six. So, five thousand, six hundred and twenty-five!

Quick review. Take the digits in front of the five. Multiply by the next number up. Put twenty-five on the end. See you next time!