Question
Mon April 14, 2014 By: Girija Bane

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

Expert Reply
Mon April 14, 2014

The answer to the second question is given below. The 'Ask the Expert' subscription  allows you to post only one question at a time. We request you to re-post the pending question again.

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

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