Question

In the following numbers, the rational number is:

• A. $\sqrt{9}$
• B. $\sqrt{3}$
• C. $\sqrt{0.1}$
• D. $0.101101110\ldots$

Hint:

If the number under the square root is a perfect square, its square root is a rational number.

Answer 1

The Correct Option is A

Step 1: Recall the definition of a rational number.
A rational number is a number that can be expressed in the form $\dfrac{p}{q}$, where $p$ and $q$ are integers and $q \ne 0$.

Step 2: Analyze each option.
(A) $\sqrt{9} = 3$, which is a rational number because it can be written as $\dfrac{3}{1}$.
(B) $\sqrt{3}$ is an irrational number because 3 is not a perfect square.
(C) $\sqrt{0.1}$ is irrational because 0.1 is not a perfect square.
(D) $0.101101110\ldots$ is a non-terminating, non-repeating decimal, so it is also irrational.

Step 3: Conclusion.
Hence, among the given options, only $\sqrt{9}$ is a rational number.