"sqrt" in UK....1 or +/-1?

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18 years ago
#21
In article <[email protected] c.uk>, Robert Low <[email protected]
ux.services.coventry.ac.uk> writes
[q1]>[/q1]
[q1]>(NB I have more confidence in your ability to quote than in the document)[/q1]
[q1]>[/q1]

Yes - I wasn't promoting the thing!

[q1]>'a positive *integer*'. Oh dear. (What stage is that?)[/q1]

This is year 8.

M.
--
Mark Houghton [email protected]
0
18 years ago
#22
Mark Houghton <[email protected]> wrote:
[q1]>O.k. - I found the "official" line in the National Numeracy Strategy document. I would've looked[/q1]
[q1]> there before, but I like to leave all these documents at work :-)[/q1]
[q1]>[/q1]
[q1]>Students should:[/q1]
[q1]>[/q1]
[q1]>"Know that a positive integer has two square roots, one positive and one[/q1]

(NB I have more confidence in your ability to quote than in the document)

'a positive *integer*'. Oh dear. (What stage is that?)

--
Rob. http://www.mis.coventry.ac.uk/~mtx014/
0
18 years ago
#23
Mark Houghton <[email protected]> wrote:
[q1]> O.k. - I found the "official" line in the National Numeracy Strategy document. I would've looked[/q1]
[q1]> there before, but I like to leave all these documents at work :-)[/q1]
[q1]>[/q1]
[q1]> Students should:[/q1]
[q1]>[/q1]
[q1]> "Know that a positive integer has two square roots, one positive and one negative; by convention[/q1]
[q1]> the square root sign denotes the positive square root."[/q1]

I second Rob's concern about "integer". Furthermore, I dislike "positive" in the last part. It
should be rewritten, perhaps as:

Know that a positive real number has two square roots, one positive and one negative; by convention,
the square root sign denotes the nonnegative square root.

David

--
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0
18 years ago
#24
Darrell <[email protected]> wrote in message
news:[email protected]...
[q1]> In the U.S. the radical with implied index of 2 (i.e. the square root symbol) is usually taken to[/q1]
[q1]> mean only the principal root, e.g. sqrt(1) is[/q1]
1,
[q1]> not -1, and -1 could be written as -sqrt(1).[/q1]
[q1]>[/q1]
[q1]> What is the convention most widely used in the UK? The context is usual maths for 16-18 years old[/q1]
[q1]> in the UK. Is sqrt(1)=1 or both 1 and -1? This is not an invitation for explanations such[/q1]
[q1]> as....there are two numbers[/q1]
whos
[q1]> square is 1. This is simply a question of the meaning of the notation "sqrt" in the UK. Thank you[/q1]
[q1]>[/q1]
[q1]> --[/q1]
[q1]> Darrell[/q1]
[q1]>[/q1]

As this is an "education.maths" group, I think the important issue here is ensuring the maths
student _understands_ about pos and neg roots - and thus uses judgement in the context of a given
problem to arrive at the correct - and more important, a sensible - answer.

See separate thread "wath is apening here ? i = 1/i -> 1 = -1 ?" to see the problems created by a
lack of understanding. No hard and fast rule will help, IMHO.

--
Martin

0
18 years ago
#25
"martin" <[email protected] k> wrote in message news:[email protected]...

[q1]> As this is an "education.maths" group, I think the important issue here is ensuring the maths[/q1]
[q1]> student _understands_ about pos and neg roots - and[/q1]
thus
[q1]> uses judgement in the context of a given problem to arrive at the[/q1]
correct -
[q1]> and more important, a sensible - answer.[/q1]

I agree of course. But it is also certainly an important issue to ensure students avoid ambiguity by
understanding the meaning of symbols. This was the spirit of my inquiry------a simple question of
the literal meaning of a specific notation. Thanks to all who have replied.

--
Darrell
0
18 years ago
#26
David W. Cantrell <[email protected]> wrote:
[q1]>Mark Houghton <[email protected]> wrote:[/q1]
[q2]>> "Know that a positive integer has two square roots, one positive and one negative; by convention[/q2]
[q2]>> the square root sign denotes the positive square root."[/q2]
[q1]>[/q1]
[q1]>I second Rob's concern about "integer". Furthermore, I dislike "positive" in the last part. It[/q1]
[q1]>should be rewritten, perhaps as:[/q1]

Actually, if we're only taking square roots of positive numbers, I don't mind the 'positive' in the
document, since I'd read 'non-negative' as explicitly allowing the possibility of 0. And presumably
they miss out the '0' case because it's the time the square roots coincide. A bit fiddly however one
does it, I guess.
--
Rob. http://www.mis.coventry.ac.uk/~mtx014/
0
18 years ago
#27
[email protected] c.uk (Robert Low) wrote:
[q1]> David W. Cantrell <[email protected]> wrote:[/q1]
[q2]> >Mark Houghton <[email protected]> wrote:[/q2]
[q2]> >> "Know that a positive integer has two square roots, one positive and one negative; by[/q2]
[q2]> >> convention the square root sign denotes the positive square root."[/q2]
[q2]> >[/q2]
[q2]> >I second Rob's concern about "integer". Furthermore, I dislike "positive" in the last part. It[/q2]
[q2]> >should be rewritten, perhaps as:[/q2]
[q1]>[/q1]
[q1]> Actually, if we're only taking square roots of positive numbers,[/q1]

If that is the case, then I agree with you. I had assumed (perhaps incorrectly) that they were also
supposed to know that the square root of zero is zero. If my assumption is correct, then the latter
part of the quotation is problematic, in effect disallowong use of the square root sign when the
radicand is zero (since zero has no positive square root).

[q1]> I don't mind the 'positive' in the document, since I'd read 'non-negative' as explicitly allowing[/q1]
[q1]> the possibility of 0. And presumably they miss out the '0' case because it's the time the square[/q1]
[q1]> roots coincide. A bit fiddly however one does it, I guess.[/q1]

Yes, a bit fiddly.

Regards,
David

--
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0
18 years ago
#28
Sorry for the typos...I was in a hurry. Please replace all radicands of "a" with radicands of "a^2."

"Darrell" <[email protected]> wrote in message
news:[email protected]...
[q1]> Thanks for the reply, but I am talking about reals only at this point. Perhaps my subject line[/q1]
[q1]> could have been formulated better. There are two square roots of a^2. The question is....does the[/q1]
[q1]> *notation* sqrt(a) (i.e. the radicand is a and the index is understood to be 2) in the UK evaluate[/q1]
to
[q1]> both a and -a, or just a? In the U.S. it is just a and if you wish to denote -a, using this[/q1]
[q1]> notation, it would be -sqrt(a), i.e. sqrt(a), which[/q1]
is
[q1]> a, multiplied by -1 giving -a (hence unambiguous.)[/q1]
[q1]>[/q1]
[q1]> The purpose of the question is to confirm or refute a UK student's claim that in the UK the[/q1]
[q1]> convention is sqrt(a) evaluates to both a and -a. My feeling is that the UK in all probability[/q1]
[q1]> follows the same convention in normal practice, i.e. 16-18 year old algebra courses. If there are[/q1]
[q1]> any current UK teachers reading this, I would appreciate your responses as I[/q1]
am
[q1]> trying to find a consensus one way or the other to confirm or refute my assumption.[/q1]
[q1]>[/q1]
[q1]> --[/q1]
[q1]> Darrell[/q1]
[q1]>[/q1]
[q1]> "Richard Battye" <[email protected]> wrote in message[/q1]
[q1]> news:[email protected]pex.com...[/q1]
[q2]> > Darrell,[/q2]
[q2]> >[/q2]
[q2]> > It's been a long time but I think you are talking about 18 yr old study.[/q2]
[q1]> At[/q1]
[q2]> > this point are we talking about complex numbers ? I am an engineer so[/q2]
know
[q2]> > it as 'j' (sqrt(-1)), in maths terms 'i', that is the UK convention. sqrt(4)=2 in most other[/q2]
[q2]> > cases. I hope I am not oversimplifying. As an 18[/q2]
[q1]> yr[/q1]
[q2]> > old math student studying maths negative roots were considered as -1 and not -sqrt(1) but, it[/q2]
[q2]> > was 16 yrs ago. -sqrt(1) looks ambiguous to me ?[/q2]
[q1]> Damn,[/q1]
[q2]> > I'm just rediscovering maths. In IT now.[/q2]
[q2]> >[/q2]
[q2]> > Rich. "Darrell" <[email protected]> wrote in message[/q2]
[q2]> > news:[email protected]...[/q2]
[q3]> > > In the U.S. the radical with implied index of 2 (i.e. the square root symbol) is usually taken[/q3]
[q3]> > > to mean only the principal root, e.g. sqrt(1)[/q3]
[q1]> is[/q1]
[q2]> > 1,[/q2]
[q3]> > > not -1, and -1 could be written as -sqrt(1).[/q3]
[q3]> > >[/q3]
[q3]> > > What is the convention most widely used in the UK? The context is[/q3]
usual
[q3]> > > maths for 16-18 years old in the UK. Is sqrt(1)=1 or both 1 and -1?[/q3]
[q1]> This[/q1]
[q3]> > > is not an invitation for explanations such as....there are two numbers[/q3]
[q2]> > whos[/q2]
[q3]> > > square is 1. This is simply a question of the meaning of the notation "sqrt" in the UK. Thank[/q3]
[q3]> > >[/q3]
[q3]> > > --[/q3]
[q3]> > > Darrell[/q3]
[q3]> > >[/q3]
[q3]> > >[/q3]
[q2]> >[/q2]
[q2]> >[/q2]
[q2]> >[/q2]
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