2020/025) How many positive perfect squares less than $10^6$ are multiples of 24?

 Because the number is a perfect square and multiple of 24 this should be multiple of smallest multiple of 24 which is a square.

Now  $24 = 2^3 * 3 $ so to get the smallest multiple of 24 which is a square we need to make the power of 2 and 3 both even or we need to multiply by 2* 3 or 6 to get 144. So we need

$144n^2 = (12n)^2 <= 10^6$ 

or $12n <= 1000$

or $n <= \frac{1000}{12}= 83.3$

So $n < =83$ and hence there are 83 numbers