Square numbers and square roots

Hello, and welcome to Myriora Maths! Can you make a perfect square out of counters? With four counters, yes. With nine, yes. With six, no! The numbers that make squares are called square numbers. Let's meet them!

Here are the first square numbers. One by one is one. Two by two is four. Three by three is nine. Four by four is sixteen. And five by five is twenty-five.

We write a square number with a small two, like this. Four squared means four times four: sixteen. It's called squared, because it makes a square!

Here's a beautiful pattern. Start with one counter. Add three, in an L shape, and you get four. Add five more, and you get nine. Add seven more: sixteen. So every square number is the odd numbers added up!

Square roots go backwards. The square root of twenty-five asks: what number, times itself, makes twenty-five? Five times five is twenty-five. So the square root of twenty-five is five. It's the length of the side of the square!

Let's try one together. What is seven squared? Say it out loud!

Seven squared is seven times seven: forty-nine! Well done if you said forty-nine!

Here's a question that catches lots of people. What is three squared? Some people say six, because they do three times two. But squared means a number times itself: three times three is nine!

Your turn! What is the square root of eighty-one? Pick the right card. You've got fifteen seconds, or pause the video. Go!

Time's up! What number, times itself, makes eighty-one? Nine times nine is eighty-one. So the square root of eighty-one is nine!

Quick review. A square number is a number times itself. One, four, nine, sixteen and twenty-five all make squares of counters. Square numbers are the odd numbers added up. And the square root goes backwards: it's the side of the square. See you next time!