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grei
Posts:
132
Registered:
11/27/12


Re: rationalize
Posted:
Jul 10, 2013 9:30 AM


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.



