Classify the following number as rational or irrational: (3+2 ) - Vidyadip

Question

Classify the following number as rational or irrational:$\big(3+\sqrt{2}\big)$

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Answer

Let $3+\sqrt2$ be rational.
Hence, 3 and $3+\sqrt2$ are rational.
$\therefore3+\sqrt{2}-3=\sqrt2=$ rational $[\because$ Difference of two rational is rational$]$
This contradicts the fact that $\sqrt2$ is irrational.
The contradiction arises by assuming $3+\sqrt2$ is rational.
Hence, $3+\sqrt2$ is irrational.

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