Question

Summation or Subtraction of rational number and irrational number is always a/an __________ number.

(a) natural

(b) whole number

(c) rational number

(d) irrational number

The question was posed to me in an online interview.

Question is taken from Representing Real Numbers on the Number Line & Real Numbers Operations in division Number Systems of Mathematics – Class 9

Answer 1

Right choice is (d) irrational number

Explanation: Let’s take one rational number and one irrational number for example.

Consider 3 and \(\sqrt{2}\)

We know that 3 is rational number and \(\sqrt{2}\) is irrational number.

By adding 3 and \(\sqrt{2}\), we get 3+\(\sqrt{2}\)

We know that \(\sqrt{2}\) = 1.414213…

Since the expansion of \(\sqrt{2}\) is non-terminating and non-recurring, expansion of 3+\(\sqrt{2}\) will also be non-terminating and non-recurring. Therefore result of summation will be irrational number.

The same will happen if we subtract \(\sqrt{2}\) from 3.

Hence we can say that Summation or Subtraction of rational number and irrational number is always irrational number.