This Square Roots Trick from TikTok Doesn't Actually Work
The math corner of TikTok produced this a couple weeks ago:
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If you don’t want to watch the video, it briefly demonstrates a shortcut you can use to find square roots. Here’s the shortcut, written formally:
Claim (TikTok Square Root Theorem): Take a 2-digit number x that you can express as ab, where a is the 10s digit and b is the 1s digit (For example, if x=27, then a=2 and b=7). The square root of x is given by a+b-2.
The video gives a few examples. If x=64 (a=6, b=4), then the square root is 6+4-2=8. This is correct: the square root of 64 is 8.
There’s just one problem: this trick doesn’t actually work.
It’s not even difficult to disprove this, because it doesn’t work for most numbers. It doesn’t work for 16 (the formula incorrectly tells us the square root of 16 is 5), 36, 49, 81, 100, 121… and so on.
You might ask why these shortcuts even matter if students can just use calculators. I believe there’s value in showing these shortcuts. Tanya Zakowich, aka Pinkpencilmath, showcased this neat formula for approximating square roots on TikTok last year. Even though, in practice, you’d never use this formula over a simple calculator, showing tricks like this is the kind of thing that gets people interested in math. It shows the patterns and structure underlying the whole field. It stokes your curiosity, because some will want to understand why the tricks work.
But that only works, if your tricks actually work.