Question
Statement-1 (Assertion): \( \sqrt{2} \) is an irrational number.
Statement-2 (Reason): The sum of a rational number and an irrational number 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
\( \sqrt{2} \) is an irrational number because it cannot be expressed as a ratio of two integers.
Also, the statement:
“The sum of a rational number and an irrational number is irrational”
is true.
However, Statement-2 does not explain why \( \sqrt{2} \) is irrational.
- Statement-1 is true
- Statement-2 is true
- But Statement-2 is not the correct explanation of Statement-1
Final Answer
✔ Correct option: (b)