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[eerr]

Honestly, I think lots of classes require a sort of hardcore development you just don't get in this day and age.

By hardcore development i mean you'd be working with other people to heavily refine skills.

I need this for a few of my other classes but... ugh.

[Nolor]

I need some math help too, actually, and this seems as good a place as any.

So I'm sure there's some really simple rule that I'm missing, but when I'm given questions like:

4√2(5√4 - 4√8)

and then asked to simplify, I haven't the faintest idea where to start. (I'm also open to a better way of formatting questions like these on the forums; here's what I meant to imply:

So basically, how do I multiply/divide monomials and binomials with radicals?

My brain shuts down when I try to visualize multiples of roots, or even represent them in any way but concretely.

[Vector]

4√2(5√4 - 4√8)

4√2(5√4 - 4√8)

4√2(5*2 - 4*2√2)

4√2(10 - 8√2)

(4√2)(10) - (4√2)(8√2)

4*10√2 - [4*8][(√2)(√2)]

40√2 - (32)(2)

40√2 - 64


Let me know if you need more help.

[Virex]

Well, if x is a positive, real (don't ask) number then √x is also a real, positive number, so it works exactly like any other number. Some other things to remember are:

2√x = √(2²x) = √4x and √x * √x = √x² = x

My brain shuts down when I try to visualize multiples of roots, or even represent them in any way but concretely.

They're just numbers, formulated oddly, albeit ellegantly, considering that √2 = 1.4142135624.... into infinity. (You also can't define it with a division, to make things extra interesting). Basicly, think of it as another way to write numbers down, with a few strings attached to the notation, as I said above. You'll run into the same thing when doing logarithms, exponents and trigionometric functions, but those have slightly weirder rules.

[ToonyMan]

They're radicals or something.

[Nolor]

So originally I was still having some problems, and tried to post a few questions. Due to forum troubles, I wound up spending about an hour or so playing around with the numbers, going through Vector's steps, etc.

I'm pretty sure I've figured it out, though I still don't have the hang of reducing radicals easily (without a calculator, that is.)

Spoiler: another question, + my solution (click to show/hide)

(There's probably an error in here somewhere.)

2√3(8√6 - 7√9)

2√3(8√6 - 21)

(2√3)(8√6) - (2√3)(21)

(2√3)(8√6) - (42√3)

(16√18) - (42√3)

(48√2) - (42√3)

[Vector]

Very good job =)  It's perfect.

[Nolor]

Thanks for your help. In retrospect, it's rather simple and makes me wonder what I was doing before. I think I just thought it was more complex than it actually is.

The relationship between roots/exponents/fractional exponents is interesting. I'm stumbling through most of this (my teacher gave me a few sheets filled with these sorts of questions and told me to work through them) but it's fun anyway.

Just one last question:

If I have something like

√60 * 2√6

I can turn it into this:

2√360

But from here, is there an easy way to simplify it? I can look it up and see that √360 = 6√10, but if I don't have a handy chart/table with me, it seems like it'd be a bit more difficult.

[Vector]

Hey, if you're stumbling, then you're doing it exactly right.  Mathematics is an art of exploration, and it's only through running into poison oak a thousand times that you'll be able to see the poetry of it all.  I'm also very glad that you're having fun!  Keep up the good work.

Now, for your new problem.  Check this out:

√60 * 2√6 = 2√(60)(6) = 2√(6)(6)(10) = 12√10

And, since 10 = (2)(5) as we know, there are no more pairs in the factorization that we can pull out.  This means it's fully simplified.  For cube roots you'll be looking for triples, for fourth roots quads of the same number, and so on.

If the problem isn't being as nice to you as that one was and you just have a big number under the radical, you need to factor the number similarly and find pairs.  This is usually done by

1. heuristics

and

2. brute force.

If you don't know what I'm talking about, I'll be more than happy to explain further.

[Nolor]

Spoiler (click to show/hide)

4√2 * √180

4√(2)(180)

4√(2)(18)(10)

4√(2)(6)(3)(10)

4√(2)(2)(3)(3)(2)(5)

4(2*3)√2*5

24√10

It makes much more sense now. At first, I wasn't quite sure why I was supposed to factor it into pairs, but then skimming through the past few posts and seeing √x² = x again, I realized what I was missing.

I certainly see the appeal of mathematics. There's nothing quite like the rush you get when you suddenly understand something you didn't before.

Thanks for your help, once again.

[Osmosis Jones]

I certainly see the appeal of mathematics. There's nothing quite like the rush you get when you suddenly understand something you didn't before.

It's why we all do it. Well, that and the satisfaction you can get turning a page of calculations into a beautiful little answer. Good onya!

[Red Fortune]

Ooooh, just had another math test, and it had a somewhat relevant question...

The only problem (or in this case, 1 point of a problem) I couldn't solve involved getting the simplest surd answer of x for:

600 = 1000 - 0.005x³

Now, from that one can get x = ³√80000, but is there an easier way to simplify other than trying all the numbers you can think of? (I ended up figuring it out, and that it's 20√10, but I went through a lot of trial and error after the test because I didn't have enough time.)

[Vector]

Ooooh, just had another math test, and it had a somewhat relevant question...

The only problem (or in this case, 1 point of a problem) I couldn't solve involved getting the simplest surd answer of x for:

600 = 1000 - 0.005x³

Now, from that one can get x = ³√80000, but is there an easier way to simplify other than trying all the numbers you can think of? (I ended up figuring it out, and that it's 20√10, but I went through a lot of trial and error after the test because I didn't have enough time.)

...

I'll just write down the mental process I go through while simplifying, and you can see if it works for you or not.

80000 = [8](10⁴) = (2³)(10³)(10).

Thus we have 3 2's and 3 10's, so we put 20√10.

[Red Fortune]

...

I'll just write down the mental process I go through while simplifying, and you can see if it works for you or not.

80000 = (8)(10⁴) = (2³)(10³)(10).

Thus we have 3 2's and 3 10's, so we put 20√10.

That works, I guess I'm just too thick to have realized it can be done that way.

[Vector]

That works, I guess I'm just too thick to have realized it can be done that way.

Hey, don't worry about it.  You've got a lot of math concepts floating around in your brain right now, and it's going to take some time and patience to fit them all together.  Just try to make your connections and figure out how the puzzle works.  You'll be fine.