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# AL rationality 1

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- ☂雨後晴空☀Lv 71 decade agoFavorite Answer
y = √3 - √2

y + √2 = √3

y^2 + 2 + 2y√2 = 3

√2 = (1 - y^2)/2y

If y = √3 - √2 is rational , that means (1 - y^2)/2y is rational ,then √2 is

rational. But we know √2 is not rational . It is impossible.

So √3 - √2 is not rational.

- 天助Lv 71 decade ago
if √3-√2 is rational, then 1/(√3-√2)=√3+√2 is rational

so,[(√3+√2)-(√3-√2)]/2=√2 is rational(contradition)

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