The difference between the square roots of a number is 30

The two square roots of any positive number have the same size,

but one is positive and the other one is negative.

Let's say the square roots of our mystery number are + S and - S.

Then the difference between them is

+S - (-S) = + S + S = 2S.

We are told that the difference between them is 30.

2S = 30

Divide each side by 2: S = 15

The positive square root of our mystery number is 15.

Our mystery number is (15) ² = 225.