Answer:
A) True  B)False  C) True  D) True  E) False  F) True
Step-by-step 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.
[tex]2\times \sqrt2 = 2\sqrt2[/tex]
C) True
For example: [tex]\sqrt2\times \sqrt2 = 2\text{ which is rational}, \sqrt2\times \sqrt3 = \sqrt6\text{ which is irrational}.[/tex]
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.
[tex]\sqrt{16} = \pm 4\text{ which is a rational number}[/tex]
F) True
Square root of a irrational number will always be irrational.
