Question

the number 3+√2 to irrational​

Answer 1

Answer:

Let us assume, to the contrary, that 3+√  2  is  rational. Then, there exist co-prime positive integers a and b such that

3+  √2 =  b a

​⇒   2 =  3ba

⇒   √2  is rational

[∵3,a and b are integers∴  3ba  is a rational number]

This contradicts the fact that   √2  is irrational.  

So, our assumption is not correct.

Hence, 3+√ 2  is an irrational number.