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Question -

Prove that √2 + √3 is an irrational number.



Answer -

Let us suppose that √2 + √3 is rational.
Let √2 + √3 = a, where a is rational.
Therefore, √2 = a – √3
Squaring on both sides, we get
 
which is a contradiction as the right hand side is a rational number while √3 is irrational.
Hence, √2 + √3 is irrational.

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