Prove that the following is irrational.
\(\frac{1}{\sqrt{3}}\)
Proof:
Assume that \(\frac{1}{\sqrt{3}}\) is .
\(\frac{1}{\sqrt{3}}\) can be expressed as where \(p\) and \(q\) are any two integers such that \(q\neq 0\)
\(\frac{1}{\sqrt{3}}=\)
On simplification we get, \(\frac{q}{p}=\sqrt{3}\)
\(\frac{p}{q}\) is as \(p\) and \(q\) are . Therefore, \(\sqrt{3}\) is
This , our assumption. \(\sqrt{3}\) is .
Hence, \(\frac{1}{\sqrt{3}}\) is .