CBSE Class 10 Mathematics Basic 2023: question 30

Hints

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Step-by-step solution

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1. Assume, on the contrary, that $3+7\sqrt{2}$ is rational. Then $3+7\sqrt{2}=\frac{p}{q}$, where $p,q$ are integers, $q\ne 0$.

   1 mark

2. $7\sqrt{2}=\frac{p}{q}-3\Rightarrow \sqrt{2}=\frac{p-3q}{7q}$.

   1 mark

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

   1 mark

Answer: $3+7\sqrt{2}$ is irrational

Revise the chapter

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