MP Board · Class 9 · Mathematics · Number SystemsOn rationalizing the denominator of $\frac{1}{\sqrt{7} - 2}$, we get:
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Step-by-Step Solution
Multiply numerator and denominator by $(\sqrt{7} + 2)$. We get $\frac{\sqrt{7} + 2}{(\sqrt{7})^2 - (2)^2} = \frac{\sqrt{7} + 2}{7 - 4} = \frac{\sqrt{7} + 2}{3}$.
Detailed Options Breakdown
Option : \frac{\sqrt{7} + 2}{3} (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 1: \frac{\sqrt{7} - 2}{3}
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Number Systems.
Option 2: \frac{\sqrt{7} + 2}{5}
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Number Systems.
Option 3: \sqrt{7} + 2
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Number Systems.
💡 Study Guide: This question tests core syllabus concepts from Number Systems. For formulas, key summaries, and mock exam reference guides, read the full Number Systems Revision Notes.