UPSKILL MATH PLUS
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Learn moreProve that the following is irrational.
\(\frac{1}{\sqrt{2}}\)
Proof:
Assume that \(\frac{1}{\sqrt{2}}\) is .
Therefore, \(\frac{1}{\sqrt{2}}\) can be expressed as
That is, \(\frac{1}{\sqrt{2}}=\)
On simplification we get,
\(\frac{p}{q}\) is as \(p\) and \(q\) are .
Therefore, \(\sqrt{2}\) is
This , our assumption.
Hence, \(\frac{1}{\sqrt{2}}\) is .
Answer variants:
\(\frac{p}{q}\)
\(\frac{p}{q}\), where \(p\) and \(q\) are any two integers such that \p q\neq 0\)
\(\sqrt{2}=\frac{p}{q}\)
\(\sqrt{2}=\frac{q}{p}\)
contradicts
irrational
rational
\(\frac{p}{q}\), where \(p\) and \(q\) are any two integers such that \(q\neq 0\)
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