UPSKILL MATH PLUS
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Learn moreVerify that \(9+4\sqrt{7}\) is irrational.
Proof:
Let \(9+4\sqrt{7} =\frac{p}{q}\) be a number, where \(p\) and \(q\) are and \(q\neq 0\)
\(4\sqrt{7}=\frac{p}{q}-9\)
\(\sqrt{7}=\frac{p-9q}{4q}\)
Since, , \(\frac{p-9q}{4q}\) will also be .
Therefore, \(\sqrt{7}\) is rational.
This the fact that \(\sqrt{7}\) is .
Hence, \(9+4\sqrt{7}\) is irrational.
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