Simplification II

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November 4th 2008, 10:55 AM
Simplicity

Simplification II

Would this simplification be correct?

$\sqrt{\frac{A^2 - 2A^2B^2+A^2B^4+4A^2B^2C^2}{1-2B^2+B^4+4B^2C^2}} = \sqrt{\frac{A^2(1-2B^2+B^4+4B^2C^2)}{1-2B^2+B^4+4B^2C^2}} = \sqrt{{A^2}} = A$
November 4th 2008, 11:20 AM
Moo

Hello,

Quote:

Originally Posted by Air

Would this simplification be correct?

$\sqrt{\frac{A^2 - 2A^2B^2+A^2B^4+4A^2B^2C^2}{1-2B^2+B^4+4B^2C^2}} = \sqrt{\frac{A^2(1-2B^2+B^4+4B^2C^2)}{1-2B^2+B^4+4B^2C^2}} = \sqrt{{A^2}} = {\color{red}|}A{\color{red}|}$

This would be better (Tongueout)
November 4th 2008, 11:59 AM
Simplicity

... And what if it was:

$\sqrt{\frac{A^2 - 2A^2B^2+A^2B^4+4A^2B^2C^2}{(1-2B^2+B^4+4B^2C^2)^2}}$

How would I simplify that?
November 4th 2008, 12:02 PM
Moo

Quote:

Originally Posted by Air

... And what if it was:

$\sqrt{\frac{A^2 - 2A^2B^2+A^2B^4+4A^2B^2C^2}{(1-2B^2+B^4+4B^2C^2)^2}}$

How would I simplify that?

Hmmm well, you'd have :

$\sqrt{\frac{A^2}{|1-2B^2+B^4+4B^2C^2|}}$ after simplifying :) (what's in a square root must be positive)

$=\frac{|A|}{\sqrt{|1-2B^2+B^4+4B^2C^2|}}$

now if you know that one or another is positive, you can remove the absolute values

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