Rationalizing
A student questions the rule of rationalizing denominators, and the teacher can't really justify it.
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Cartoon by Ben Orlin, Math with Bad Drawings. https://cartoons.mathwithbaddrawings.com/2018-01-22-rationalizing/ (CC BY-NC 4.0)Transcript
Teacher: "Always write √2/2; never 1/√2." Student: "Why? Isn't it simpler?" Teacher: "It's not about simple." Student: "Isn't it called 'simplifying'?"
Teacher: "No, it's called 'rationalizing the denominator.'" Student: "Then why not rationalize the numerator? Or is that too... rational?"
Teacher: "You ask a lot of questions." Student: "You don't give a lot of answers."