Question

Prove that √2 + 1/√2 is an irrational number

Answer 1

Answer:

To prove: 2root2 - 1 irrational.

Let us assume that 2root2 - 1 is rational so,

2root2 - 1 = a/b (a and b are co prime)

2root2 = a/b+1 = a+b/b

Now,

Root2 = a+b/2b

BUT we know that root2 is irrational

So 2root2 - 1 is also irrational

Hence, our assumption was wrong.

Hence proved!!

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