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

Let 2  +  √2be a rational number say r.
Then,2  +  √2=r
√2=r - 2
But, √2is an irrational number.

LHS is irrational thus RHS should also be irrational to maintain the equality.

Therefore, r – 2 is also an irrational number
⇒ r is an irrational number.
Hence our assumption r is a rational number is wrong.
Hence, 2  +  √2 is not a rational number.

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