Sum of rational and irrational numbers is

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Irrational

Rational

Both

None of these

answer is A.

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Detailed Solution

Given a rational and irrational number.
A rational number is a number that can be in the form

p q

, where p and q are integers and q is not equal to zero.
Irrational number are those which cannot be expressed in fractional form, i.e.

p q

form, they neither terminate nor do they repeat. they are also known as a non-terminating number.
Let us assume that the sum of a rational number and an irrational number is a rational number.
We know that a rational number can be expressed in the form of

p q

where p,q are any integers and q is not equal to zero.
So, we can express our assumption as :

p q + x = a b

where x is irrational.

x = a b − p q

So, x is a rational number, but that contradicts our starting assumption.
Hence, the sum of a rational numbers and an irrational number is irrational.
The sum of a rational number and an irrational number is irrational.
Therefore, the correct option is 1.

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