What type of number is this $\frac{\sqrt2}{2}$? $$\frac{\sqrt{2}}{2}$$
In this monomial, an irrational number is divided by a rational number. However this is not a general case but can any one tell me that when we divide an irrational number or multiply an irrational number or its multiplicative inverse by a rational number then what type of the number we get in output? Either rational or irrational?

Suppose that $\frac{\sqrt{2}}{2}=\frac{p}{q}$, then $\sqrt{2}=\frac{2p}{q}$, hence $\sqrt{2}$ would be rational, this is clearly a contradiction.
