Why does the answer key sometimes have a different form compared to my solution?

[romsofia]

Are you seriously saying that if you program $1/\sqrt 2$ a computer should return a computational error?

Of course not, but would I write down $\frac{1}{\sqrt{2}}$ on a math exam? Nope. In a similar vein, would you stop at $\sqrt{80}$, or would you write $4\sqrt{5}$? $\frac{7\sqrt{10}}{\sqrt{2}}$ or $7\sqrt{5}$? Let's make it more algebraic, $\frac{1}{i-\sqrt{3}}$ or $-\frac{i+\sqrt{3}}{4}$? $\ln(x^3)$ or $3\ln(x)$? $\ln(-1)$ or $i\pi$? None of these matter to a computer! If you're against reducing as a whole, I get the point.

Now, would I take points off an exam? No, I'm a physicist, I personally don't care. Numbers are numbers. But, if you write something down in the form of a ratio, you follow the definition of rational numbers.

Do I think students get tired of it? Of course.

 

[PeroK]

I would guess none. If that is all it takes to turn someone off mathematics, he wasn't into it in the first place.

I would profoundly disagree with that attitude on a number of levels. First, that could be a reason that women are discouraged from studying mathematics. You would need some educational research to settle the matter, but it may be that women generally think more flexibly and are put off by that sort of hidebound thinking. In fact, your post in this day and age is quite explicitly sexist, as you assume the student is a "he".

More generally, that sort of attitude prevents fresh blood from entering institutions or professions. There is a certain type that inhabits the profession and they are at pains to ensure those entering the profession are of the same type.

 

[PeroK]

Of course not, but would I write down $\frac{1}{\sqrt{2}}$ on a math exam? Nope. In a similar vein, would you stop at $\sqrt{80}$, or would you write $4\sqrt{5}$?

There is nothing to choose between $\sqrt{80}$ and $4\sqrt{5}$. They are both equally simple.

$\frac{7\sqrt{10}}{\sqrt{2}}$ or $7\sqrt{5}$?

$7\sqrt{5}$ is clearly simpler. Whereas, there is no sense in which $\frac {\sqrt 2} 2$ is simpler than $\frac 1 {\sqrt 2}$. This is why, outside of your dictatorship (e.g. in the realm of QM), $\frac 1 {\sqrt 2}$ is preferred. E.g. in the so-called singlet state:

https://en.wikipedia.org/wiki/Singlet_state#Singlets_and_entangled_states

I don't believe for one minute that quantum physicists fail to grasp the basics of elementary mathematics. Just because they don't obey your hidebound conventions.

No, I'm a physicist, I personally don't care.

I'm struggling to understand you now, as there is definitely no such convention in physics as the one you claim. Pick up any QM book if you don't believe me.

 

[martinbn]

E.g. in the so-called singlet state:

https://en.wikipedia.org/wiki/Singlet_state#Singlets_and_entangled_states

There is a difference. Here it is normalizing a vector, so it is better to see it as $\frac{\vec{a}}{||a||}$.

 

[martinbn]

I would profoundly disagree with that attitude on a number of levels. First, that could be a reason that women are discouraged from studying mathematics. You would need some educational research to settle the matter, but it may be that women generally think more flexibly and are put off by that sort of hidebound thinking. In fact, your post in this day and age is quite explicitly sexist, as you assume the student is a "he".

More generally, that sort of attitude prevents fresh blood from entering institutions or professions. There is a certain type that inhabits the profession and they are at pains to ensure those entering the profession are of the same type.

I really don't know how to respond to this. May be you need to calm down a bit.

 

[FactChecker]

Could it be because it is easier to do the calculation by hand? If calculating the long division by hand, I would prefer $\sqrt{2}/2 = 1.414213.../2 = 0.707106...$ over $1/\sqrt{2}=1/1.414213... =$? (just seems harder)
So maybe it's just a left-over from the days before calculators.

 

[PeroK]

Could it be because it is easier to do the calculation by hand? If calculating the long division by hand, I would prefer $\sqrt{2}/2 = 1.414213.../2 = 0.707106...$ over $1/\sqrt{2}=1/1.414213... =$? (just seems harder)
So maybe it's just a left-over from the days before calculators.

Exactly. Which is why the attempts to ridicule the alternative have, quite frankly, made me angry.

 

[berkeman]

Pausing the thread for a bit, and some possible Moderation...

 

[berkeman]

Just to tie off this thread, there may be times when one form or another of a solution is preferred or required, such as:

** The denominator needs to be rationalized -- this is required on some university problems and exam questions

** The denominator does not need to be rationalized, since the fraction is expressing the sides of a triangle so the fraction is intuitive the way it is

** The final numerical answer needs to be computed without the aid of a calculator, and one form of the fraction is more amenable to that hand calculation

Thread will remain closed.