Answer:
A) True B)False C) True D) True E) False F) True
Explanation:
We are given the following information in the question:
A is a rational number and B is an irrational number.
A) True
The sum of A and B will always be irrational.
B)False
We will show this with the help of a counter example.
2 is a rational number and √2 is an irrational number but their product is irrational.

C) True
For example:

D) True
Square of a rational number will always be a rational number.
E) False.
We will prove thus with the help of a counter example.

F) True
Square root of a irrational number will always be irrational.