Let $f\left(x\right)=\left[x^2\right]\sin \pi x,x\in R,$ the number of points in the interval $(0,3]$ at which the function is discontinuous is_____(where [.] denotes G.I.F)

$$\begin{gathered} f\left(x\right)=0<x<1= \sin \pi x 1\le x<\sqrt{2} \\ =2\sin \pi x \sqrt{2}\le x<\sqrt{3} \\ = 3\sin \pi x \sqrt{3}\le x<2 \\ = 4\sin \pi x 2\le x<\sqrt{5} etc. \end{gathered}$$

The function is discontinuous at $x=\sqrt{2},\sqrt{3},\sqrt{5},\mathrm{.......}\sqrt{K}$ where K is not a perfect square. Points of discontinuity (desired) = $\sqrt{2},\sqrt{3},\sqrt{5},\sqrt{6},\sqrt{7},\sqrt{8}.$