# Transcendental number

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Transcendental numbers are necessarily irrational, but there are many irrational numbers that are not transcendental. For instance, ${\displaystyle {\sqrt {2}}}$ is irrational. However it is algebraic, since it is a root of the polynomial ${\displaystyle x^{2}-2}$. It is thus irrational but not transcendental.
Proving a number to be transcendental is generally much more difficult than just proving it is irrational. Examples of real numbers known to be transcendental are ${\displaystyle \pi }$ and ${\displaystyle e}$.