Is 343 a square number

Answer 1

343 = 7 cubed, so it's not the square of an integer. (It's almost exactly the square of 18.52)

Two further thoughts:

No number ending in 2, 3, 7 or 8 can be the square of an integer;

A cube can also be a square only if the original number was a square.

eg (22)3 = 64 which is (23)2. The law of powers means that the cube of x squared is x6

and the square of x cubed is also x6.

Try this: if x to the power y - y to the power x = 1, what are x and y?