Question

Sum of a rational and an irrational number is a/an

• A. rational number
• B. irrational number
• C. real number
• D. We can't add a rational and an irrational number

Answer 1

Answer: (B), (C)

The correct options are
B

irrational number

C

real number

Sum of a rational and an irrational number is always an irrational number.

Example:

Consider a raitonal number: $4$

and an irrational number: $\mathrm{2.7582463023874529....}$ [The numbers after decimal are non-terminating and non-recurring]

When we add these two numbers, we get,

$4+\mathrm{2.7582463023874529....}=\mathrm{6.7582463023874529....}$, which is also an irrational number as the numbers after decimal are non-terminating and non-recurring.

Since, all the rational as well as irrational numbers are real numbers, so, the resultant sum is also a real number.