The difference can be rational or irrational.
5 + sqrt(3) and 2 + sqrt(3) are both Irrational Numbers but their difference is
[5 + sqrt(3)] - [2 + sqrt(3)] = 3, which is rational.
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No. sqrt(3) - sqrt(2) is irrational.
To the lower number, add an irrational number that is less than the difference. For example, if the difference between the two numbers is 0.001 (1/1000), you can add the square root of 2 divided by 2000; pi divided by 4000, or the number "e" divided by 3000, to the lower number.
Find the difference between the two numbers, then add an irrational number between zero and one, divided by this difference, to the lower number. Such an irrational number might be pi/10, (square root of 2) / 2, etc.
The difference is that rational numbers can be expressed as fractions whereas irrational numbers can not be expressed as fractions.
There is no difference. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.