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

Question

Harshit Singh · Answer

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

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

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

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