We have recently done a unit on perfect squares in school. The following conversation with Katie (8yo) happened completely spontaneously on a peaceful, evening ride home.

K: 10,000 is a double perfect square.

Me: What do you mean?

K: Well, 100 is already a perfect square, and 10,000 is 100 times 100.

Me: I see. Can you think of another double perfect square.

K: Yeah, 81.

Me: Indeed. Now, double perfect squares are also called perfect fourth powers.

K: What does that mean?

Me: It means that you can get them by multiplying a number by itself 4 times.

K: I don’t really understand.

Me: Well, 100 is 10 times 10 so 100 times 100 is 10 times 10 times 10 times 10, that is, 10 times itself 4 times. So what is 81 the fourth power of?

K: 3, because it is 3 times 3 times 3 times 3.

Me: Yep. Now if a number can be obtained by multiplying some number by itself 3 times, then it is called a perfect cube.

K: How come?

Me: Well it has something to do with cubes. Why don’t you think about it.

I am totally going to use the term “double perfect square” now!

To be continued…

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## About aofradkin

I enjoy thinking about presenting mathematical concepts to young children in exciting and engaging ways.

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