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Show by proof of contradiction that root 3 - root 2 is not rational?
I know how to use PoC to show that root 2 is irrational but i'm not sure how to do root 3 - root 2, help please!!
1 Answer
- Ron WLv 71 decade agoFavorite Answer
Suppose there are positive integers m and n such that
√3 - √2 = m/n
Then
(√3 - √2)² = m²/n²
5 - 2√6 = m²/n²
(5n² - m²)/(2n²) = √6
Since 5n² - m² and 2n² are integers, this implies that √6 is rational. If you have already established the irrationality of √6, you're done; otherwise, it's essentially the same approach as proving the irrationality of √2.
