MiniMath Roots - Eddie Scheurer '27

Have you ever played one of those (admittedly bad) “merge genre” phone games? They are surprisingly similar to root numbers. I believe that root numbers are one of the most poorly taught concepts of Math. The reason I believe this is because they are taught without properly explaining anything:

√4=2

√100=10

√8=2√2

√4096=64

^3√8=2

Why does a three there change that? There’s usually a two there? Why is two, and not one the assumed number there?

Rather let’s think about root numbers as a different type of number: ones with a protective shield around them. The protective shields stop lower-level functions from working, so you can’t use either addition or subtraction on root numbers:

√2+√3=√2+√3

but their shields fail when a mid-to-high-level function is used, so multiplication, division, exponents, etc. can be used between root numbers. Like those merge games, when you “combine” (multiply) two of the same root number, it becomes a “normal” number:

√2×√2=2

√5×√5=5

√𝜋×√𝜋=𝜋

√12÷√2=√6

√12÷2=√12÷2

But what does the three in that exponent-esque spot earlier do? It just tells you how many you need to “merge” together, and it can be assumed that you only need to combine two when there is no goal listed:

^3√4×^3√4×^3√4=4

^3√7×^3√7×^3√7=7

√5×^3√5×^3√5×^3√5×^3√5=5 √5 ^3√5

Root numbers were just the original merge games all along.