Question

Which of the following statements is/are correct about irrational numbers?
(A) The sum of two rational numbers is always irrational.
(B) \(\pi\) is an irrational number.
(C) The value of \(\sqrt{49}\) is an irrational number.
(D) The value of \(\sqrt{5}\) is an irrational number.
Choose the correct answer from the options given below:

• A. (A),(B) and (C) only
• B. (A), (B) and (D) only
• C. (A), (B), (C) and (D)
• D. (B) and (D) only

Hint:

Sum of rationals is rational, and \(\sqrt{49} = 7\) is rational. Keep only B and D.

Answer 1

The Correct Option is D

Step 1: Idea:
Test each statement with a definition or a quick example, and keep only those that survive.

Step 2: Statement (A) by counter example:
Take the rational numbers 2 and 3. Their sum is 5, which is rational. One example is enough to show that "always irrational" is wrong.

Step 3: Statement (C) by simplifying:
$\sqrt{49} = 7 = \dfrac{7}{1}$. It is written as a fraction, so it is rational and (C) fails.

Step 4: Statements (B) and (D):
$\pi$ is a famous irrational number. $\sqrt{5}$ is the root of a number that is not a perfect square, so it is irrational too. Both hold.

Step 5: Pick the option:
The true set is {B, D}. Only option 4 lists exactly this pair.

Final Answer:
The correct choice is (B) and (D) only. \[ \boxed{\text{(B) and (D) only}} \]