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If we add or subtract two irrational numbers, we get __________ number.(a) natural(b) rational(c) irrational(d) rational or irrationalI had been asked this question during an interview.The above asked question is from Representing Real Numbers on the Number Line & Real Numbers Operations topic in portion Number Systems of Mathematics – Class 9

Answer»

Correct option is (d) rational or irrational

To explain: Let’s take two irrational numbers to understand this.

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

By adding these, we get \(\sqrt{2}\) + (-\(\sqrt{2}\)) = 0

Which is rational number SINCE it is terminating.

Now, consider \(\sqrt{5}\) and \(\sqrt{2}\)

By adding these, we get \(\sqrt{5}\) + \(\sqrt{2}\)

Which is irrational since the EXPANSION of √5 and √2 is non-terminating and non-recurring.

Now, let’s take two numbers for subtraction.

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

By subtracting these, we get \(\sqrt{2} – \sqrt{2}\) = 0

Which is rational number since it is terminating.

Consider \(\sqrt{5}\) and \(\sqrt{2}\)

By subtracting these, we get \(\sqrt{5}\) – \(\sqrt{2}\)

Which is irrational since the expansion of \(\sqrt{5}\) and \(\sqrt{2}\) is non-terminating and non-recurring.

Hence, we can say that if we ADD or subtract two irrational numbers, we get rational or irrational number.


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