Help with inverse proportions The value of $y$ varies inversely as $\sqrt x$ and when $x=24$, $y=15$.
What is $x$ when $y=3$?
I'm having trouble on this and I don't get why it's not $\frac{2\sqrt6\cdot15}{3}=10\sqrt6$?
Am I misinterpreting the problem? This is how I learned inverse proportion so I'm really unsure.

Your mistake is you got $\sqrt x=10\sqrt6$ and not $x=10\sqrt6$. You must square to get $x=600$.
For your note, here is an elaborative answer.


 Two variable quantities $x$ and $y$ are said to be inversely proportional if and only if their product is a constant. Symbolically,
$$x\propto\frac1y\iff xy=k$$
for some constant $k$.


Now, for the given problem, we should have $y\sqrt x=k$. Now, putting the given values, $k=15\sqrt{24}$. Finally, for $y=3$,
$$3\sqrt x =15\sqrt{24}\implies\boxed{x=600}$$


Hope this helps. Ask anything if not clear :)
