Prove that \(10+3\sqrt{7}\) is an irrational.
Proof:
Assume \(10+3\sqrt{7}\) is .
If \(10+3\sqrt{7}\) is rational, it can be written as a fraction
\(\sqrt{7}=\)
Here, both and \(3q\) are integers.
Therefore, is a rational number.
This implies that \(\sqrt{7}\) is a number.
This contradicts the fact that \(\sqrt{7}\) is .
Therefore, \(10+3\sqrt{7}\) is an .
Answer variants:
\(p-10q\)
\(\frac{p}{q}\), where \(p\) and \(q\) are integers and \(q= 0\)
\(7p-q\)
\(4-3q\)
\(\frac{p-10q}{3q}\)
rational
\(\frac{q+10p}{3+p}\)
irrational
\(\frac{p}{q}\), where \(p\) and \(q\) are integers and \(q\ne 0\)