Irrational problem: prove 5^(1/3) - 3^(1/4) is irrational

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lifeofpai

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Hey,
I need to prove that the number \(\displaystyle \, \sqrt[3]{\strut \,5\, }\, -\, \sqrt[4]{\strut \,3\,}\, \)irrational.

from :McGraw-Hill - Advanced Calculus 2002
 
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lifeofpai said:
Hey,
I need to prove that the number \(\displaystyle \, \sqrt[3]{\strut \,5\, }\, -\, \sqrt[4]{\strut \,3\,}\, \)irrational.

from :McGraw-Hill - Advanced Calculus 2002
Click to expand...

Can you prove that √2 is irrational?
 
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