Show that \(11\sqrt{2}\) is irrational.
Proof:
Let \(11\sqrt{2}\) is .
\(11\sqrt{11}\) can be expressed as form
\(11\sqrt{11}=\) be number, where \(p\) and \(q\) are and \(q\neq 0\)
On simplification we get, \(\sqrt{11}=\frac{\frac{p}{q}}{11}\)
Since, \(p\) and \(q\) are integers, \(\frac{\frac{p}{q}}{11}\) will also be .
Therefore, \(\sqrt{11}\) is .
This the fact that \(\sqrt{11}\) is .
Hence, \(11\sqrt{11}\) is .