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Prove that the following are irrationals: 7√5??????????????????????????

Prove that the following are irrationals: 
7√5??????????????????????????

Grade:12

1 Answers

Harshit Singh
askIITians Faculty 5963 Points
3 years ago
Dear Student

Let us assume7√5is a rational number.
Then we can find co-prime a and b (b ≠ 0) such that7√5= x/y Rearranging, we get,
√5= x/7y
Since, x and y are integers, thus,√5is a rational number, which contradicts the fact that√5is irrational. Hence, we can conclude that7√5is irrational.
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Thanks

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