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Question
Show that the following numbers are irrational.
Solution
Let us assume that `6+sqrt2 ` is rational. Then , there exist positive co primes a and b such that
`6+sqrt2=a/b`
`sqrt2=a/b-6`
`sqrt2=(a-6b)/b`
Here we see that `sqrt2` is a rational number which is a contradiction as we know that `sqrt2` is an irrational number
Hence `6+sqrt2`is irrational
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