Which of the following statements is/are correct about irrational numbers?
(A) The sum of two rational numbers is always irrational.
(B) π 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:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (B) and (D) only
An irrational number is a number that cannot be written as \(\frac{p}{q}\) with integers \(p\) and \(q\ne0\); its decimal form never ends and never repeats. The square root of a whole number is rational only when the number is a perfect square.
(A) The sum of two rational numbers is always irrational. Incorrect. The sum of two rational numbers is always rational: adding \(\frac{a}{b}\) and \(\frac{c}{d}\) gives \(\frac{ad+bc}{bd}\), again a ratio of integers.
(B) π is an irrational number. Correct. \(\pi=3.14159\ldots\) never ends or repeats; \(\frac{22}{7}\) is only a value close to it.
(C) The value of \(\sqrt{49}\) is an irrational number. Incorrect. 49 is a perfect square, so \(\sqrt{49}=7\), which is rational.
(D) The value of \(\sqrt{5}\) is an irrational number. Correct. 5 is not a perfect square, so \(\sqrt{5}=2.2360\ldots\) cannot be written as \(\frac{p}{q}\).