Question

If the following statement is True, enter 1 else enter 0.

The difference between these two irrational numbers, $7+5\sqrt{2}$ and $-3+5\sqrt{2}$ is rational.

Answer 1

To get the difference as rational, the numbers need to have an irrational part which should be same and of the same sign such that they cancel each other while subtracting.
The given pair of numbers are $7+5\sqrt{2}$ and $-3+5\sqrt{2}$
After subtracting we get,
$=>7+5\sqrt{2}-(-3+5\sqrt{2})=7+5\sqrt{2}+3-5\sqrt{2}=10$
It is an rational number.