Answer:
The product of two rational numbers is rational, and the sum of two rational numbers is irrational.
Explanation:
Let be
and
rational numbers whose forms are, respectively:
and
,
,
,
,

We proceed to demonstrate if the Pythagorean sum of two rational numbers leads to a rational number.
1)
,
,
,
,
,
Given.
2)
Given.
3)
1) in 2)
4)
Definition of division.
5)

6)

7)

8)
Definition of division.
9)

10)
/Result.
If
is a rational number, then
, so that
. Which means that
will be rational number if and only if the square root of
is an entire number.
Which means that correct answer is B.