prove that reciprocal of irrational is irrational
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Answered by
43
take an irrational number as 1.01001000100001....... and do reciprocal of it. it will be 1 upon 1.01001000100001........ and 1.01001000100001..... cannot divide 1 so reciprocal of irrational number is irrational number
Answered by
88
The reciprocal of any irrational number is irrational.
Proof: Let x be an irrational number.
Then 1/x = a/b where a and b are integers, a ≠ 0 (since 0 is a rational number) and b ≠ 0. x = 1/1/x = 1/a/b = b/a where b and a are integers and a ≠ 0.
Proof: Let x be an irrational number.
Then 1/x = a/b where a and b are integers, a ≠ 0 (since 0 is a rational number) and b ≠ 0. x = 1/1/x = 1/a/b = b/a where b and a are integers and a ≠ 0.
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