CBSE Class 10 Mathematics Basic 2024: question 26

Hints

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Step-by-step solution

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1. Assume, to the contrary, that $6+3\sqrt{2}$ is rational. Then $6+3\sqrt{2}=x$, where $x$ is a rational number.

   1 mark

2. $3\sqrt{2}=x-6\Rightarrow \sqrt{2}=\frac{x-6}{3}$

   1 mark

3. Since $x$ is rational, $\frac{x-6}{3}$ is rational, so $\sqrt{2}$ would be rational. This contradicts the given fact that $\sqrt{2}$ is irrational. Hence our assumption is wrong, and $6+3\sqrt{2}$ is irrational.

   1 mark

Answer: $6+3\sqrt{2}$ 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