You have seen that √2 is not a rational number. Show that 2 +√2 is not a rational number.

Let 2 +√2 be a rational number say r.
Then 2 +√2 =  r
√2 =  r -2
But,√2 is an irrational number.
Therefore,   r - 2 is also an  irrational number.
=> r is  an  irrational number.
Hence our assumption r  is a rational number is wrong.

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