SOLUTION: Knowing that Sqrt(2) is not a rational number, prove that 1-(1/Sqrt(2)) is not a rational number.

Question 1033666: Knowing that Sqrt(2) is not a rational number, prove that 1-(1/Sqrt(2)) is not a rational number.
Found 2 solutions by robertb, ikleyn:
Answer by robertb(5830)   (Show Source): You can put this solution on YOUR website!
Suppose is a rational number. Then it can be expressed as the ratio of two positive, relatively prime whole numbers a and b such that . (It is safe to assume that b > a.)

But if this were the case, then , a ratio of two whole numbers. Contradiction.
Hence must also be irrational.
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
Knowing that Sqrt(2) is not a rational number, prove that 1-(1/Sqrt(2)) is not a rational number.
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    - Proving irrationality of some real numbers
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