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

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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) About Me  (Show Source):
You can put this solution on YOUR website!
Suppose 1-1%2Fsqrt%282%29 is a rational number. Then it can be expressed as the ratio of two positive, relatively prime whole numbers a and b such that 1-1%2Fsqrt%282%29=+a%2Fb. (It is safe to assume that b > a.)

But if this were the case, then sqrt%282%29+=+b%2F%28b-a%29, a ratio of two whole numbers. Contradiction.
Hence 1-1%2Fsqrt%282%29 must also be irrational.

Answer by ikleyn(52781) About Me  (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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