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Teachers often take off points from students who write 1/sqrt(2) instead of sqrt(2)/2. Why do we need to write it as sqrt(2) / 2 ? Where did that convention come from? Do we need to even do it? Why do teachers care so much?

Nina Mallalieu
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    because it is difficult to divide $1$ by $\sqrt{2}$ but it is fairly easy to divide $\sqrt{2}$ by $2$, isn't it? – b00n heT Apr 27 '15 at 22:24
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    I have never seen this requirement, nor teachers taking points off at least at the university level. I would find it also very odd since both are perfectly equivalent. The only reason I could imagine is that the form is explicitly required in the exam, to see if students can do the conversion. But there is no other reason in my opinion. – Andreas H. Apr 27 '15 at 22:32

2 Answers2

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Why do we need to rationalize fractions?

To put it simply, you don't. Not in practical life, anyway. Rationalizing or not, the value of the number is the same. However, there is an advantage of rationalizing. Consider, for example, the number $1/\sqrt{2}$. It is known that $\sqrt{2} \approx 1,4142...$. I'll sort of answer your question with another one: if you want to estimate $1/\sqrt{2}$, what is easier? To think that $$\frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2} \approx 0,7071...$$ or trying to compute $$\frac{1}{\sqrt{2}}\approx \frac{1}{1,4142...}$$ is some way?

Ivo Terek
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There is no mathematical reason, it is one of "penmanship."

My hypothesis is that it makes grading easier for them, since requiring this will standardize the answers they get into one form, allowing them to mark the answers that match that form "correct" and those that don't "incorrect" without actually numerically evaluating the answers that may be numerically correct, but didn't match their desired form.

Jonathan Hebert
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  • I would say that there are reasons, but they only emerge in later mathematics, like complex numbers/analysis, and integration. (In particular, finding real and imaginary parts requires rationalisation.) – Chappers Apr 27 '15 at 22:31