- #1
Jef123
- 29
- 0
1. Prove that [itex]\sqrt{2}[/itex] is not a rational number using the rational zero theorem
2. Homework Equations : x2-2
So, I was thinking to just show that the only rational numbers that have the form [itex]\frac{c}{d}[/itex] are [itex]\pm[/itex] 1, [itex]\pm[/itex] 2, but [itex]\sqrt{2}[/itex] is not any of those numbers, so it must be irrational? I feel like I'm supposed to have more of a justification as to why [itex]\pm 1, 2[/itex] are the only possible numbers
2. Homework Equations : x2-2
The Attempt at a Solution
So, I was thinking to just show that the only rational numbers that have the form [itex]\frac{c}{d}[/itex] are [itex]\pm[/itex] 1, [itex]\pm[/itex] 2, but [itex]\sqrt{2}[/itex] is not any of those numbers, so it must be irrational? I feel like I'm supposed to have more of a justification as to why [itex]\pm 1, 2[/itex] are the only possible numbers