Prove that \(\sqrt{17} + \sqrt{21}\) is an irrational.
Proof:
Assume \(\sqrt{17} + \sqrt{21}\) is
If \(\sqrt{17} + \sqrt{21}\) is rational, it can be written as \(\sqrt{17} + \sqrt{21}=\) , where \(p\) and \(q\) are integers. and \(q\neq 0\).
on both sides we get,
\(\sqrt{357}=\frac{p^2-38}{2q^2}\)
Here,\(p^2\),\(38\),\(2q^2\) are . Therefore,\(\frac{p^2-38}{2q^2}\) is number .
This implies that \( \sqrt{357}\) is number.
This contradicts the fact that \(\sqrt{357}\) is .
Therefore, \(\sqrt{17} + \sqrt{21}\) is an .