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Prove that the following are irrationals: 1/√2 ??????????????????????

Prove that the following are irrationals:
1/√2 ??????????????????????

Grade:12

1 Answers

Harshit Singh
askIITians Faculty 5963 Points
3 years ago
Dear Student

Let us assume1/√2is rational.
Then we can find co-prime x and y (y ≠ 0) such that1/√2= x/y Rearranging, we get,
√2= y/x
Since, x and y are integers, thus,√2is a rational number, which contradicts the fact that√2is irrational. Hence, we can conclude that1/√2is irrational.
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Thanks

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