What is the lowest number 588 can be multiplied by so that the result is a squared number?

The lowest number is 3.

3 x 588 = 1,764

1,764 = (42) squared

I don't know an easy way to do it. I just slogged through it one-by-one ...

I tried 2, then I tried 3 and I didn't have to go any farther.

You could have done the same thing. The difference between us is that

I'm willing to work on it just for fun, whereas you're not willing to work on it

even for homework. That's why I became good in math and you might not.