What is the square root of 16?

The most read post I’ve ever written on this blog explains what the square root of 16 is. Most of the traffic to that post comes from search engines, which seems to indicate that a lot of people are curious about square roots. All that I’ve written on the subject before is in Norwegian, which of course means that most of the world can’t understand it, but square roots are really important and should be known by everyone. That’s why I’m writing this post in a language that is understood over a much greater part of the world.

A square root is often denoted by the radical sign, or √. The use of the word square is far from arbitrary. Let me illustrate a point using a few US pennies I’ve got lying around. To be more exact, three of them. See how I managed not to fit them into a square. If I wanted to make a square that was two pennies along each side, I’d have needed one more penny, to a total of four. This means that the square root of three must be less than two. Its real value actually a weird number that can’t be expressed as a total of (countable) pennies, practically worthless as they may be. The most accurate way to express the value is, actually, as √3.

Three pennies not in a square
These coins are so worthless you just leave them on the ground in Norway so I get to find them.

Let’s try that thing again with a different currency. I found nine Norwegian 50-øre, a coin which used to be worth about as much as a US dime, or ten US pennies. But the bank got rid of it because people considered them practically worthless and nobody cared about them (lesson to US citizens: get rid of the penny, it’s worth ten times less and actually useless). Anyway, as you can see, nine 50-øre fit neatly into a square that’s three coins along each side. This demonstrates that the square root of nine is, in fact, exactly three.

Nine 50-ører in a nice square
Now that these coins are not used anymore, the only nynorsk coin left is the femkrone.

Finding the exact square root of 16 is left as an exercise to the reader.


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