Show that \(11\sqrt{41}\) is irrational.
Proof:
Let \(11\sqrt{41}\) is .
By definition, \(11\sqrt{41}\)
That is, \(11\sqrt{41}=\) be number, where \(p\) and \(q\) are and \(q\neq 0\)
On simplification we get, \(\sqrt{41}=\frac{\frac{p}{q}}{11}\)
Since, \(p\) and \(q\) are integers, \(\frac{\frac{p}{q}}{11}\) will also be .
Therefore, \(\sqrt{41}\) is .
This the fact that \(\sqrt{41}\) is .
Hence, \(11\sqrt{41}\) is .