# What type of number is this

What type of number is this $\frac{\sqrt{2}}{2}$?
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talhekh
Suppose that
$\frac{\sqrt{2}}{2}=\frac{p}{q}$
with $p$ and $q$ integers. Multiply through by $2$ to get
$\sqrt{2}=\frac{2p}{q}$
That would make $\sqrt{2}$ be rational, which it's not. So the assumption that $\frac{\sqrt{2}}{2}$ is rational must be wrong.
More generally: irrational divided by rational is still irrational.