Question

Irrational number in the following will be

• A. \(\sqrt{25}\)
• B. \(\sqrt{81}\)
• C. \(\dfrac{5}{3}\)
• D. \(5 + \sqrt{2}\)

Hint:

If any expression contains a non-terminating, non-repeating decimal (like \(\sqrt{2}\)), the result is irrational.

Answer 1

The Correct Option is D

Step 1: Evaluate each option.
\(\sqrt{25} = 5\) (rational), \(\sqrt{81} = 9\) (rational), \(\frac{5}{3}\) (rational), \(5 + \sqrt{2}\) (irrational).
Step 2: Reasoning.
A sum of a rational number and an irrational number is always irrational.
Step 3: Conclusion.
Hence, \(5 + \sqrt{2}\) is the only irrational number among the options.