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Prove 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