How would I find the square root of 49531.25 without a calculator?

well, without a calculator, what you can do is

round each choice to a "metric" value, namely 312.5 use 310, and then you can simply multiply it manually 310*310, which is 96100, well, that's too large, so nope.

don't bother with 323.4 because that's even larger.

likewise, check 239.3 with say 230 * 230, to see if it's close enough.

then check 222.5 with 220*220.

That's a good question for google haha