CBSE Class 10 Mathematics Basic 2024: question 23(a)

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Step-by-step solution

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1. Assume, on the contrary, that $-7-2\sqrt{3}$ is rational, say $-7-2\sqrt{3}=r$, where $r$ is rational. Then $2\sqrt{3}=-7-r\Rightarrow \sqrt{3}=\frac{-7-r}{2}$

   1 mark

2. Since $r$ is rational, $\frac{-7-r}{2}$ is rational, so $\sqrt{3}$ would be rational. This contradicts the given fact that $\sqrt{3}$ is irrational. Hence our assumption is wrong, and $-7-2\sqrt{3}$ is irrational.

   1 mark

Answer: $-7-2\sqrt{3}$ 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