Question

How are rational and irrational numbers related?

Answer 1

Hint: We first describe the rational and irrational numbers. We express the binary operations’ form for rational and irrational numbers. We find that there are no relations between them. We express that through examples to conclude the solution.

Complete step by step solution:
We first describe the terms rational and irrational numbers and show examples to understand the concept better. Real number sets can be expressed in two parts and they are rational and irrational numbers. In combination they make the whole real number set.
We can express any rational number in the form of $\dfrac{p}{q},\left[ p,q\in \mathbb{Z},q\ne 0 \right]$.
The terms p and q are in their simplest form and that’s why they both can’t be even. One or both of them has to be odd.
Any kind of binary operations between two rational numbers is always a rational number.
Examples of rational numbers are $\dfrac{5}{4},0.417,0.4\overline{92},0,-5$.
Any other number not being a rational number is called an irrational number.
In most of the cases binary operations between two irrational numbers is an irrational number. Exceptions being the numbers are same for subtraction, multiplication and division and same number with opposite sign for addition.
Examples of irrational numbers are $e,\pi ,\sqrt{11}$.
Therefore, they are not related in any ways.

Note: Rational and Irrational numbers both are real numbers but different with respect to their properties. Rational numbers are finite and repeating decimals whereas irrational numbers are infinite and non-repeating. In short, we can say that rational and irrational numbers are mutually exclusive but jointly or collectively exhaustive set of real numbers.