MLeszega
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Hey guys. I forget where I found this problem but it goes as follows: Prove that \sqrt[3]{2} cannot be represented in the form p+q\sqrt{r} where p,q, and r are rational numbers.
It is easy to show that \sqrt[3]{2} is irrational, so it cannot be put in the form m/n, where m and n are integers. However, I do not know where to go from here. I figured that since \sqrt[3]{2} is irrational it cannot be put in any form using rational numbers, but I am not sure.
Any help is appreciated, thanks in advance.
It is easy to show that \sqrt[3]{2} is irrational, so it cannot be put in the form m/n, where m and n are integers. However, I do not know where to go from here. I figured that since \sqrt[3]{2} is irrational it cannot be put in any form using rational numbers, but I am not sure.
Any help is appreciated, thanks in advance.