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Show that \frac{3+\sqrt{7}}{5} is an irrational number, given that \sqrt{7} is irrational.

 

 

 

 
 
 
 
 

Answers (1)

Let given is rational

So,

\frac{3+\sqrt{7}}{5}=\frac{p}{q}

\sqrt{7}=\frac{5p-3q}{q}

Hence \frac{5p-3q}{q} is rational it means that \sqrt{7} is also rational, but we know that \sqrt{7} is irrational. This contradicts our assumption that \frac{3+\sqrt{7}}{5} is rational. Hence it is irrational.

Posted by

Ravindra Pindel

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