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Re: Radical Multiplication

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Dan Cass

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Dec 9, 2009, 1:08:55 PM12/9/09
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> Has anyone ever seen such a triple radical
> multiplication question? See attachment.

At the site I saw the expression
sqrt(2^109)*sqrt(x^306)*sqrt(x^11).
If the question is to simplify this, note
one can do the multiplications first, then squareroot
of the result. Also 2^109 = 2*2^108, and
x^11 = x*x^10.

So we get sqrt( 2*2^108 * x^306 * x*x^10 )
which simplifies to 2^54 * x^158 *sqrt(2*x).

It looks like one of those questions from intro algebra...

Dan Cass

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Dec 9, 2009, 1:09:12 PM12/9/09
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Pubkeybreaker

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Dec 10, 2009, 11:00:37 AM12/10/09
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On Dec 9, 1:08 pm, Dan Cass <dc...@sjfc.edu> wrote:

> So we get sqrt( 2*2^108 * x^306 * x*x^10 )


> which simplifies to 2^54 * x^158 *sqrt(2*x).

Why is this latter expression any simpler than

Y = sqrt(2^109 * x^317)?

It seems to me that Y is a simpler expression. Certainly
it contains fewer symbols.

Why does "simply" mean:

Express as the product of the square root of a square free expression
and
another expression extracted as the square root of an exact square.

What makes this "simpler"?


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