I am a three digit number. My middle number is double the other two which are square numbers. The number is what?

There's only 4 numbers which fit the first part of the question

121

242

363

484

Only the last one 484 has square numbers at the beginning and end (4 is 2 squared). 3 and 2 are not square numbers. 1 is 1 squared, so 121 is sort of right, but 1 doesn't usually count as a square number as it's unique

484 there you go my guy

I think 484 is your answer