If f(x) = 5x – 10 is divided by x –$\sqrt{2}$, then the remainder will be :

Let's divide f(x) = 5x – 10 by x –$\sqrt{2}$:

$\frac{5\mathrm{x} - 10}{x-\sqrt{2}}$= $\frac{5(\mathrm{x} - 2)}{x-\sqrt{2}}= \frac{5(\sqrt{x}-\sqrt{2}) (\sqrt{x} +\sqrt{2})}{x-\sqrt{2}}$

As we can see, after dividing the equation with x –$\sqrt{2}$ , we will not get the quotient in p/q form, therefore, we can say that it is a irrational number.