Greetings from Brasil...
Follow the reasoning.
288 ÷ 2 = 144
and 144 its a perfect square (144 = 12²)
It is visible that if we multiply 288 by 1/2, we will obtain a perfect square, but we will do this via a simple equation
288 · X = 144
X = 144 ÷ 288
X = 0,5 ⇔ X = 1/2