Honestly, I want to know. Who is writing this stuff?
8th grade pre-algebra
OK, so I read this several times and finally understood what they wanted. Keep in mind, this was a "no calculator" test.
I'll explain: every square root has two answers, one positive and one negative.
For example, √25 = ±5, because (-5) x (-5) also equals 25.
So, without a calculator (why, and why would anyone have to calculate this anyway?) the students needed to find a number with a square root of about 1/2 of 5.3, so that the difference between the positive square root and the negative square root equals about 5.3.
One of the most pointless questions I've seen to date.