\frac{1}{\sqrt{2}} is a rational number.
Multiplying and dividing numerator and denominator by √2 we get,
\frac{1}{\sqrt{2}}\times\frac{\sqrt{2}}{\sqrt{2}}=\frac{\sqrt{2}}{2}(∵\sqrt{2}\times\sqrt{2}=2)
We know that, √2 = 1.4142…
Then, \frac{\sqrt{2}}{2}=\frac{1.4142}{2}=0.7071..
Since the number , 0.7071..is non-terminating non-recurring, \frac{1}{\sqrt{2}} is an irrational number.
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