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Topic: rationalize
Replies: 1   Last Post: Jul 10, 2013 9:30 AM

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Posts: 132
Registered: 11/27/12
Re: rationalize
Posted: Jul 10, 2013 9:30 AM
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That's going to be difficult. Typically, with cube roots, you use the cube formula (x+ y)(x^2- xy+ y^2)= x^3+ y^3
so that if x= cbrt(a) and y= cbrt(b)
(cbrt(a)+ cbrt(b))(cbrt(a^2)- cbrt(a)cbrt(b)+ cbrt(b^2)= a+ b.

With THREE cuberoots like that, separate them:
(cbrt(a)+ (cbrt(b)+ cbrt(c)) and multiply numerator and denominator by (cbrt(a^2)- cbrt(a)(cbrt(b)+ cbrt(c))+ (cbrt(b)+ cbrt(c))^3)= a+ (cbrt(b)+ cbrt(c))^3\

Of course, ((cbrt(b)+ cbrt(c))^3 is NOT just "b+ c". It is, rather, b+ 3cbrt(b^2)brt(c)+ 3cbrt(b)cbrt(c^2)+ c
so you have to continue to get rid of those cuberoots.

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