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Article #31

Re: Need Urgent Help - surds

#31
From: Sid_Moir
Date: Fri, 09 Apr 1999 00:00
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Siobhan Michaels wrote:

>
> Also, i can't grasp the topic of surds and could anyone help me with that??
> Thanx
> --
> Siobhan
>         X
> ICQ:32493520

An abreviated explanation from Australia for you, Siobhan.

Let me start by defining a few terms.
A surd is a 'square root' number.  I don't know how to write a square root sign
in this program so let me pretend it is R.   R will stand for my square root
sign. 'Like' terms are terms that are similar, so R3 and 5*R3 are similar terms
because both have R3, but R2 and R3 are not similar so are called 'unlike'
terms.
Now R3 or R24 or R25 are have square root signs so are all surds. (R25 is
called a surd in this format even though it can be simplified to an integer of
5 - in the form of R25 it IS a surd)
One usually cannot add or subtract surds that are different (called unlike
terms), so R3 + R5 cannot be simplified. But one can multiply or divide unlike
terms - such as R3 * R5 = R(3*5) = R15,  or R24 / R2 = R(24/2) =R12.
Furthermore, one can simplfy some surds.  R25 = 5 obviously, so R75 =
R(25*3)=R25 * R3 = 5 * R3
Similarly, some unlike surds can be added/ subtracted after simplifying them,
for example R8 + R18.
This is because R8= R(4*2)=R4 * R2 =2 *  R2.
Similarly R18 = R(9*2) = R9 * R2 = 3 * R2.
So R8 + R18 = 2*R2 + 3*R2 = 5*R2  (or since 5 = R25, then 5*R2 could become R25
* R2 = R(25*2) = R50)
So you see that we could have 'simplified' R8 + R18 to be equal R50.
When a number is written entirely as a surd ( R2 or R50 or R16 etc.) it is
called an entire surd. If we had a term such as 3R2, we change it 3 = R9, then
can simplify 3R2 = R9 * R2 = R(9*2) = R18.

Hope this helps - it is very condensed.
Sid


>

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Siobhan Michaels wrote:
<blockquote TYPE=CITE>&nbsp;
<br>Also, i can't grasp the topic of surds and could anyone help me with
that??
<br>Thanx
<br>--
<br>Siobhan
<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; X
<br>ICQ:32493520</blockquote>

<p><br>An abreviated explanation from Australia for you, Siobhan.
<p>Let me start by defining a few terms.
<br>A surd is a 'square root' number.&nbsp; I don't know how to write a
square root sign in this program so let me pretend it is R.&nbsp;&nbsp;
R will stand for my square root sign. 'Like' terms are terms that are similar,
so R3 and 5*R3 are similar terms because both have R3, but R2 and R3 are
not similar so are called 'unlike' terms.
<br>Now R3 or R24 or R25 are have square root signs so are all surds. (R25
is called a surd in this format even though it can be simplified to an
integer of 5 - in the form of R25 it IS a surd)
<br>One usually cannot add or subtract surds that are different (called
unlike terms), so R3 + R5 cannot be simplified. But one can <u>multiply</u>
or <u>divide</u> unlike terms - such as R3 * R5 = R(3*5) = R15,&nbsp; or
R24 / R2 = R(24/2) =R12.
<br>Furthermore, one can simplfy <u>some</u> surds.&nbsp; R25 = 5 obviously,
so R75 = R(25*3)=R25 * R3 = 5 * R3
<br>Similarly, some unlike surds <u>can</u> be added/ subtracted after
simplifying them, for example R8 + R18.
<br>This is because R8= R(4*2)=R4 * R2 =2 *&nbsp; R2.
<br>Similarly R18 = R(9*2) = R9 * R2 = 3 * R2.
<br>So R8 + R18 = 2*R2 + 3*R2 = 5*R2&nbsp; (or since 5 = R25, then 5*R2
could become R25 * R2 = R(25*2) = R50)
<br>So you see that we could have 'simplified' R8 + R18 to be equal R50.
<br>When a number is written entirely as a surd ( R2 or R50 or R16 etc.)
it is called an <u>entire surd</u>. If we had a term such as 3R2, we change
it 3 = R9, then can simplify 3R2 = R9 * R2 = R(9*2) = R18.
<p>Hope this helps - it is very condensed.
<br>Sid
<br>&nbsp;
<blockquote TYPE=CITE>&nbsp;</blockquote>
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From: Sid_Moir <Sid_Moir@wollongong.apana.org.au>
Subject: Re: Need Urgent Help - surds
Date: 1999/04/09
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