Question

The sum of two rational numbers is rational and the sum of a rational number and an irrational number is irrational what about the sum of two irrational numbers decide whether the sum of two irrational numbers is always rational always irrational or either rational or irrational depending on the case share your

Answer 1

When you add two irrational numbers together, you get an irrational number. It's like if you do pi+pi and obviously you still can't write it as a fraction. Hope this helps.

Answer 2

The sum of two irrational numbers is always a irrational number

Explanation:

You can take the number π+π and the result still is an irrational number,

you can also probe with a more common number like √2 and √3, thus, we always have an irrational result.

Remember, an irrational number is the one that can not be expressed as a fraction between two integers numbers, or has an infinite number of non repetitive decimals.