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Prove that the following are irrationals: 6 + √2????????????????????

Prove that the following are irrationals: 
6 + √2????????????????????

Grade:12

1 Answers

Harshit Singh
askIITians Faculty 5963 Points
2 years ago
Dear Student

Let us assume6 +√2is a rational number.
Then we can find co-primes x and y (y ≠ 0) such that6 +√2= x/y⋅
Rearranging, we get,
√2= (x/y) - 6
Since, x and y are integers, thus (x/y) - 6 is a rational number and therefore,√2is rational. This contradicts
the fact that√2is an irrational number.
Hence, we can conclude that6 +√2is irrational.

Thanks

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