Rational number is a real number which can be expressed as a ratio of two integer numbers.

For example,

Certain numbers like √2 is not expressible in the form of ratio of integers. So it is not a rational number.All fractional numbers and integers are rational numbers.

All rational numbers can be expressed as ratio of two integers that are co-prime (relatively prime to each other). That means that, the integers do not have common factors.

When we have to prove x is a rational number, then assume that

. Then after squaring or repeated multiplication or arithmetic operations or rationalization, if you can prove that p and q are not integers or some other rule about factorization is violated, then our assumption about\

is wrong.

This is the contradiction method. You assume and arrive at a contradiction.

If q has a factor(2√5-3), then it is not an integer.