Prove that \(\frac{2\sqrt{3}}{5}\) is an irrational.
Proof:
Assume \(\frac{2\sqrt{3}}{5}\) is
Therefore, \(\frac{2\sqrt{3}}{5}=\)
On simplification, \(\sqrt{3}=\)
Since \(p\) and \(q\) are integers, \(\frac{5p}{2q}\) is a number.
This implies that \(\sqrt{3}\) is a number.
But this contradicts the fact that \(\sqrt{3}\) is .
Therefore, \(\frac{2\sqrt{3}}{5}\) is .
Answer variants:
\(\frac{2p}{5q}\)
\(\frac{5p}{2q}\)
rational
irrational
\(\frac{p}{q}\), where \(p\) and \(q\) are integers and \(q\ne 0\).
\(\frac{p}{q}\), where \(p\) and \(q\) are integers and \(q= 0\).