Exactly! Or when you're making a game about ants where you have to use toilet paper to build bridges for them and have to choose the point to attach the TP in advance and need a check which will compare the distance to that point with the amount of TP in your inventory and... yeah.

Yeah, I see, you're all smart... :P
Now, seriously, here we can see why this is a great community: everybody is trying to help event that the question is a bit childish.

Maths, bah. Numbers are overrated anyway (I give them a 3 out of 10).

Seriously, who needs them ?

I've got a little bit of a learning disorder with regards to sequencing things and confusing 6s and 9s and what not. So, I've gotten in the habit of leaving things like radicals as is as long as I can, and then look for ways of combining them or canceling them.

Even for folks without a learning disorder it makes it a lot easier to check your work later on if you get an incorrect or unexpected result.

But, at this stage I'm about 3 classes away from being able to teach high school math, so there you go.

Which is why numbers become far less important in many branches of higher mathematics (not number theory, obviously).

Good point, although I like to interpret this "which is why" as a measure of security against the k-bomb threat.

Actually I just remembered that when I was younger, I'd wondered about this question too. Of course by the time I started learning higher level math and subsequently econs, I'd more or less answered my question :P

@OP Btw I re-read my post and it sounds quite snarky to me. Was my bedtime before I'd typed the reply. If it comes across that way to you, I apologize.

In bachelor level mathematics, number crunching takes a back seat, yes.

The properties of numbers doesn't as it's the cornerstone of algebra and the basis for analysis which is used to prove calculus.

If you do any sort of algebraic manipulation, you are using numbers directly to quantify variables in your equation at the very least.

And if you go into probability and statistics, numbers are pretty much all over the place, though computers are used to do the crunching as samples can get quite large.

It's good to know you'll teach that part right to your students.

I had arguments with some of my math teachers in high school over this back in the days.

Trust me, I've seen what incompetent instruction does to students. I've spent years undoing that sort of damage.

It's one thing to ding a point for stupid errors and quite another to take all the points away. Unfortunately, with the number of problems which teachers in the US are expected to assign, it makes it quite difficult to ask the students to do things step by step line by line.

And ultimately, the only way you get really good at it is by doing a large number of varied problems, which students don't generally have time to do.

OTOH, if you completely dispense of all the numbers and the formulas, the human brain is capable of a shocking level of accuracy, very quickly for things like ballistic motion and probability.

To demonstrate a relationship between values. It's trivial to say 3 = sqrt(9). But what about sqrt(7)? It becomes an irrational number. Irrational numbers go on to infinity while the sqrt representation is much simpler to see the direction the author is taking.

Because the square roots of some numbers aren't actually real numbers or whole numbers. Also the square root can make some further algebra easier to visually see.

I whole heartily agree that this is a great community!

- However -

The question isn't even a bit childish. Your presumption is rude, but please, follow my reasoning:

If a square root is not a replacement for a specific number, and irrational numbers cannot be resolved, there is a flaw in the accuracy of every mathematical system that uses the square root. If a square root must be used to represent an approximation then the concept of accuracy ceases to be absolute and becomes relative.

I am a 41 year old, second year college student taking algebra for the first time since I was a high school sophomore. What's more, I'm a philosophy major, so the choice to accept an approximation needs to be validated as a choice, rather than a cop out.

In order to have that make sense in my own mind, I had to ask the question, "what is the actual purpose of a square root." Most people only look as far as how one is used, I want to know why it even exists in the first place.

Does that make sense?

With that in mind I turned to the smartest group of people I knew that would actually have a great chance of knowing the answer without being snide or rude.

With the exception of you, this is exactly what I have encountered.
BEST!

MATH!

ANSWER!

EVER!

That is precisely the point, because sometimes representing another way loses the accuracy or may lose the method by which you derived that number, so marking it as sq. root 7 (for example) allows you to later factor out that value or more easily work with it. However, be it noted, that sq. root 7 is a perfectly valid number, it's simply written in a fashion as to make it more useful to us (much like we don't often use binary or hexadecimal, it's not as useful for humans).

I don't want to be snarky and say, "You'll understand why in Calculus"... but, that's actually probably true, by Calculus you'll understand exactly why we use it.

Since this is a math thread I might as well jump in. I always enjoyed math in school but never really excelled at it because we hardly learned any tips, tricks or decent memory solution to easen the burden but nevertheless; there's a question that always eluded me.

What's the opposite of zero?

When you explain, you can keep in mind that I've read courses on basics when it comes to algebra, calculus and imaginary numbers but that's where it stops.

I'm sure this is the kind of question you can't really answer or requires more mathemathical knowledge than I've but humour me, I take a bad or weird answer before nothing. ;)