The first thing I think when I see this is what is the closest square number that I know close to 355?
That would be 400 which is 20².
355 is clearly less than 400 so the next smallest square number would be 19² which is 361.
361 is still bigger than 355 so the next smallest square number would be 18² which is 324.
Now 324 is less than 355 and 361 is bigger than 355 the square root of 355 must lie between the square roots of the two numbers.
Therefore, √355 must be between 18 and 19.
