Question

The difference of a rational number and an irrational number is _[blank]_ a rational number.

Which word correctly fills in the blank to create a true statement?

-sometimes

- never

- always

Answer 1

never a rational number

Answer 2

Never

Explanation:

A Rational Number is a number of the form
`(p)/(q)`, p & q are integers and q ≠ 0.

An irrational number is all real number except rational numbers i.e. it is a non-repeating and non-terminating decimal number or it can not be expressed in a ratio of two integers.

Further, Natural numbers can be a rational number.

Also, all repeating and terminating decimals are rational.

The difference of rational number and irrational number is never a rational number. For example:

2 - √3 is always an irrational number where 2 is rational and √3 is an irrational number.

Hence addition and subtraction of rational and irrational number is never a rational number it will be irrational number always.