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by Chris Burke
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1066: Strange Square Roots
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Mr. Michael Keegan, Math Teacher

Do NOT show my students this! They might think it's a rule and not a curiosity!

In fact, as strange as it looks, it isn't the only mixed number that has this property. And there isn't any reason to drop a jaw to the desk to figure out the pattern.

Let x be the whole number and y be the fraction (between 0 and 1, exclusive).

Then the equation says that (x)(sqrt(y)) = sqrt(x + y).
Square both sides we get (x2)(y) = x + y.
Subtract y from both sides (x2)(y) - y = x.
Factor the left side (y)(x2) - 1) = x.
Finally, divide y = x/(x2) - 1).

So you can pick any whole number value of x -- 2, 3, 10, whatever -- and substitute on the right side. You will get a value of y which is the fractional part of the mixed number that makes the "strange" square root work.

On a historical note: This is comic #1066. If you thought I'd do something about The Battle of Hastings ... well, it had crossed my mind, but too complicated and no way to plan in advance with the crazy schedule I'm keeping.


Please visit my blog: http://mrburkemath.blogspot.com.
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