Radical ideal of $(x,y^2)$ 
How does one show that the radical of $(x,y^2)$ is $(x,y)$ over $\mathbb{Q}[x,y]$?

I have no idea how to do, please help me.

HINT $\: $ Applying the basic laws $\  \rm r({\frak a}+{\frak b})\ =\ r(r({\frak a}) + r({\frak b}))\:,\ $ and $\rm \ \ r({\frak p}^n)\ =\ {\frak p}\:$ for prime $\frak p$ 
$\quad {\rm r}(x,y^2)\: =\: {\rm r}({\rm r}(x),{\rm r}(y^2))\: =\: {\rm r}(x,y)\: =\: (x,y)\ $ since $\:x,y,(x,y)$ are all prime in $\:\mathbb Q[x,y]\:.$
