Question

If we add or subtract an irrational number and a rational number (non-zero), then we get a/an __________ number.

(a) natural

(b) rational

(c) irrational

(d) rational or irrational

I had been asked this question during an interview.

My question is based upon Representing Real Numbers on the Number Line & Real Numbers Operations in chapter Number Systems of Mathematics – Class 9

Answer 1

The correct choice is (c) irrational

Easiest explanation: Let’s take two non-zero numbers to understand this. One rational and one irrational number.

Consider two numbers, 3 and \(\sqrt{2}\)

Adding these two, we get 3 + \(\sqrt{2}\)

Now, \(\sqrt{2}\) = 1.414213…

Expansion of √2 is non-terminating, hence result of 3 + \(\sqrt{2}\) would be non-terminating and non-recurring.

The same will happen while subtracting this.

Hence, we can say that if we add or subtract an irrational number and a rational number (non-zero) then we get an irrational number.