Statement A (Assertion): √3+ √5 is an irrational number. Statement B (Reason): √p+ √q is an irrational number, if p and q are prime natural number. a. Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) b. Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A) c. Assertion (A) is true but reason (R) is false d. Assertion (A) is false but reason (R) is true.
Question
Statement A (Assertion): √3+ √5 is an irrational number. Statement B (Reason): √p+ √q is an irrational number, if p and q are prime natural number. a. Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) b. Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A) c. Assertion (A) is true but reason (R) is false d. Assertion (A) is false but reason (R) is true.
Solution
The correct answer is (c). Assertion (A) is true but reason (R) is false.
Here's why:
Statement A (Assertion): √3+ √5 is an irrational number. This is true. The sum of two irrational numbers can be irrational, and in this case, √3 and √5 are both irrational numbers, so their sum is also irrational.
Statement B (Reason): √p+ √q is an irrational number, if p and q are prime natural number. This is false. The sum of two square roots of prime numbers is not necessarily irrational. For example, √4 + √9 = 2 + 3 = 5, which is a rational number. Therefore, the reason does not correctly explain the assertion.
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