- #1
MLeszega
- 20
- 0
Hey guys. I forget where I found this problem but it goes as follows: Prove that [tex]\sqrt[3]{2}[/tex] cannot be represented in the form p+q[tex]\sqrt{r}[/tex] where p,q, and r are rational numbers.
It is easy to show that [tex]\sqrt[3]{2}[/tex] 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 [tex]\sqrt[3]{2}[/tex] 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 [tex]\sqrt[3]{2}[/tex] 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 [tex]\sqrt[3]{2}[/tex] is irrational it cannot be put in any form using rational numbers, but I am not sure.
Any help is appreciated, thanks in advance.