Question

Find difference between $7+5\sqrt{2}$ and $-3+5\sqrt{2}$

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.

Example, the pair of numbers $7+5\sqrt{2}$ and $-3+5\sqrt{2}$ have the difference $7+5\sqrt{2}-(-3+5\sqrt{2})=7+5\sqrt{2}+3-5\sqrt{2}=10$ which is a rational number.