Prove that the following are irrational numbers
1. root 2 + root 5
2. root 3 + root 5
3. root 2 + 2 root 3
4. 2 root 2 + 3 root 3
3 root 2 - 5 root 3
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Let us assume on contrary that is a rational number.
Then there exists co-prime positive integers p and q such that
is a rational number
But this contradicts the fact that is irrational.
So, our assumption is wrong.
Hence, is irrational