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Suppose not. Then \(\sqrt 2\) is equal to a fraction \(\frac{a}{b}\text{.}\) Without loss of generality, assume \(\frac{a}{b}\) is in lowest terms (otherwise reduce the fraction). So,

\begin{equation*} 2 = \frac{a^2}{b^2} \end{equation*}

\begin{equation*} 2b^2 = a^2\text{.} \end{equation*}

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