Question

\(\frac{1}{\sqrt{2}}\) is ______ .

• A. Natural number
• B. Rational number
• C. Irrational number
• D. An Integer

Answer 1

The Correct Option is C

To solve this problem, we need to classify the number \( \frac{1}{\sqrt{2}} \).

1. Understanding the Denominator:
We know that \( \sqrt{2} \) is an irrational number, meaning it cannot be expressed as a ratio of two integers and its decimal form is non-terminating and non-repeating.

2. Dividing by an Irrational Number:
When 1 is divided by an irrational number \( \sqrt{2} \), the result is also irrational. Thus:

\[ \frac{1}{\sqrt{2}} \text{ is an irrational number.} \]

3. Evaluating Given Options:

• (1) Natural number – Incorrect; natural numbers are positive integers like 1, 2, 3, etc.
• (2) Rational number – Incorrect; the number cannot be expressed as a ratio of two integers.
• (3) Irrational number – Correct; as shown above.
• (4) An Integer – Incorrect; it's not a whole number.

Final Answer:
The correct answer is (C) Irrational number.