henrysun909@[EMAIL PROTECTED]
writes:
> Hello again.
>
> I am looking at the XAM practice book for the math CSET, which I hope
> to take in July. In it is the following problem:
>
> [6 + 2sqrt(3)] / [4 - sqrt(6)] (sorry if I have gotten the
> conventions wrong).
This notation is all right.
> [6 + 2sqrt(3)] x [4 + sqrt(6)] / [4 - sqrt(6)] x [4 + sqrt(6)] =
Here some would insist on parentheses below the line, because they
think that ab/cd = (ab/c)d = abd/c, and you mean ab/(cd). I think this
is still fine, as long as the intended meaning is understood the same
way by both of us.
The following, though, require parentheses:
> 24 + 8sqrt(3) + 2sqrt(18) + 6sqrt(6) / 16 - 6 =
> 24 + 8sqrt(3) + 6sqrt(2) + 6sqrt(6) / 10 =
> 12 + 4sqrt(3) + 3sqrt(2) + 3sqrt(6) / 5 = 6.10386
Taken as written, these would be read as a + b + c + (d/e) - f, if you
see what I mean. So write (a + b + c + d) / (e - f) instead.
> The book's answer is:
>
> -3sqrt(2) -9sqrt(3) -3sqrt(6) - 12 = -39.179
>
> Can someone confirm to me that the book's answer is wrong?
Two suggestions. First, look at the original expression. It has to be
positive! Try to see why, without actually calculating or simplifying
anything. You could also try to estimate the result in a rough way: it
seems like the stuff above the line would be something like 9 and the
stuff below the line something like 1.5, maybe, with the ratio near 6,
so the magnitude of the book answer seems also off.
Second, enter the original expression into a calculator. I used a
Scheme interpreter, and got 6.10386262914886, which agrees with you.
(You have to know how to use your calculator, of course, and it is
still good if you can spot wildly inaccurate results in case you typed
it wrong.)
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