Two statements, namely, Assertion (A) and Reason (R). Choose the correct option in context of the given statements.

Assertion(A): $3$ is an irrational number.

Reason(R): An irrational number neither terminates nor repeats, but extends to infinity.

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Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

Assertion (A) is true and Reason (R) is false.

Assertion (A) is false and Reason (R) is true.

answer is A.

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Detailed Solution

Here, we are given an assertion that

3

is an irrational number, and the reason for the same is given that it neither repeats nor terminates itself.
As per the standard definition, an irrational number is such a real number which can never be expressed as a fraction or as a ratio of two integers say

p q

, where q is non-zero.
Now, if we analyze the decimal expansion of

3

, which is 1.73205088…., we can conclude that it is neither
terminating nor repeating. So, according to the definition of irrational numbers, it is an irrational number.
Thus, the assertion and reason both are true and both complement each other.
Hence, the correct option is (1).

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