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Question -

Prove that тИЪ2 + тИЪ3 is an irrational number.



Answer -

Let us suppose that тИЪ2 + тИЪ3 is rational.
Let тИЪ2 + тИЪ3 = a, where a is rational.
Therefore, тИЪ2 = a тАУ тИЪ3
Squaring on both sides, we get
┬а
which is a contradiction as the right hand side is a rational number while тИЪ3 is irrational.
Hence, тИЪ2 + тИЪ3 is irrational.

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