Question
Statement-1 (Assertion): \( \sqrt{3} \) is an irrational number.
Statement-2 (Reason): The square root of a positive integer which is not a perfect square is an irrational number.
Options:
(a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
(b) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
(c) Statement-1 is true, Statement-2 is false.
(d) Statement-1 is false, Statement-2 is true.
Solution
\( 3 \) is not a perfect square.
Hence, its square root:
\[ \sqrt{3} \]
is an irrational number.
Statement-2 gives the general rule that explains why \( \sqrt{3} \) is irrational.
- Statement-1 is true
- Statement-2 is true
- Statement-2 correctly explains Statement-1
Final Answer
✔ Correct option: (a)