CBSE Class 10 Mathematics Standard 2024: question 25(A)

Hints

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Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

1. Assume, to the contrary, that $5-2\sqrt{3}$ is rational. Then $5-2\sqrt{3}=\frac{a}{b}$, where $a,b$ are integers and $b\ne 0$.

   ½ mark

2. Rearranging: $2\sqrt{3}=5-\frac{a}{b}=\frac{5b-a}{b}$, so $\sqrt{3}=\frac{5b-a}{2b}$.

   ½ mark

3. Since $a$ and $b$ are integers, $\frac{5b-a}{2b}$ is rational. That would make $\sqrt{3}$ rational, which contradicts the given fact that $\sqrt{3}$ is irrational.

   ½ mark

4. So our assumption is wrong. Hence $5-2\sqrt{3}$ is an irrational number.

   ½ mark

Answer: $5-2\sqrt{3}$ is irrational (proved by contradiction).

Revise the chapter

• Chapter: Real Numbers (notes, formulas, where marks are lost and every past question)
• Topic: Proving Numbers Irrational