Answer:
The product of two rational numbers is rational, and the sum of two rational numbers is irrational.
Step-by-step 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.