3 + $\sqrt{2}$ is a/an __________ number. A. natural B. irrational

Question

3 + $\sqrt{2}$ is a/an __________ number. A. natural B. irrational C. rational D. whole I had been asked this question in a national level competition. This question is from Representing Real Numbers on the Number Line & Real Numbers Operations topic in portion Number Systems of Mathematics – Class 9

fahmy · Accepted Answer

Correct choice is B. irrational The explanation: $\sqrt{2}$ = 1.414213… Since the expansion of √2 is non-terminating and non-recurring, result of 3 + $\sqrt{2}$ would be also non-terminating and non-recurring. So we can say that 3 + $\sqrt{2}$ is an irrational number.