Roots of joy?

Here's what I love.

This whole series of math opinions.

This one goes into imaginary numbers. Ahhhh....imaginary numbers. My kiddos can explain that i is imaginary and imaginary is the opposite of real numbers.

Because if you have real numbers, you must have unreal numbers.

But I have one slight problem with the opinionator's mathematical argument for why the square roots of negative numbers are imaginary. He discusses it in a purely "integer rule" sense. When you multiply two numbers together with the same sign, you get a positive sign.

Now, I've thought about the roots of negative numbers for a while. And I've thought about teaching the square roots of positive numbers to young children and have come to realize that you must have a visual representation for all of math if you want all kids to have the chance to understand.

Now, we think about square roots as the side length of squares. Think about it : 2 squared is 4, the area of a square with side length of 2 is 4. 3 squared = 9, hmmm...I wonder what the area of that square is.

Thus, you have a visual way of teaching squaring numbers and finding the square roots of numbers using area.

And here is where my argument comes in. The square root of a negative number has to be imaginary because how would one draw a square with a side length of -3? Side lengths are positive. Check out the distance formula. You know, absolute value and stuff.

Hmmm....so I have found another argument for the reasoning of i. ahhh....I'm a math nerd.