MP Board · Class 10 · Mathematics · Real NumbersWhich of the following is an irrational number?
📊Student Analytics & Stats
Total Attempts: 13
Accuracy Rate: 30.8%
Step-by-Step Solution
The correct answer is C ($5 + \sqrt{2}$).
Explanation:
- $3 + \sqrt{9} = 3 + 3 = 6$ (Rational)
- $\sqrt{25} = 5$ (Rational)
- $5 + \sqrt{2}$ is the sum of a rational number and an irrational number, which is always irrational.
- $\frac{2}{3}$ is a rational number.
Detailed Options Breakdown
Option : 3 + \(\sqrt{9}\)
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Real Numbers.
Option 1: \(\sqrt{25}\)
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Real Numbers.
Option 2: 5 + \(\sqrt{2}\) (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 3: \(\frac{2}{3}\)
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Real Numbers.
💡 Study Guide: This question tests core syllabus concepts from Real Numbers. For formulas, key summaries, and mock exam reference guides, read the full Real Numbers Revision Notes.