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?

Let $a$ irrational and suppose $b=\dfrac{n}{m}a$ ( $n,m \in \mathbb{Z}$) be rational i.e. $b= \dfrac{p}{q}$ ( $p,q \in \mathbb{Z}$).
You have:
$$
\dfrac{p}{q}=\dfrac{n}{m}a \Rightarrow a=\dfrac{pm}{qn}
$$
that is rational : contradiction!
