Question

prove that sum of two irrational number is irrational

Answer 1

Hii..

here is answer:--

To prove :- Sum of two irrational number is an irrational

Take two irrational number like,

√2 and √3

These are the irrational numbers because they are non termanating and non recurring.

So, adding √2 and √3 we get,

√2+√3 = √5

The decimal expansion of √5 is 2.2360679.........

This expansion is non termaneting andnon recurring.

We know that the number which decimal expansion is non termanating and non recurring is an irrational number.

Therefore, √5 is an irrational number.

So, the sum of two irrational is an irrational number

Hence, Proved.

Hope it helps!!