Question

Prove that 1/3+√3 is irrational​

Answer 1

sum of rational and an irrational number is is always irrational

Answer 2

Answer:

Let us assume that 1/3+sqrt3 is a rational number.

=> 1/3+sqrt 3=a where 'a' is a rational number

=> sqrt3= a-1/3

Here 'a' is a rational number and we know that 1/3 is also a rational number.

=> a-1/3 is also a rational number.

=> sqrt3 is a rational number.

But it contradicts the fact that root 3 is an irrational number.

Thus, our assumption is wrong.

Therefore 1/3+sqrt3 is an irrational number.