Your answer would be 19 and 20.
To solve this, you need to first think about perfect square numbers, and which ones are the closest to 375. This is because perfect squares will always get square rooted back to a whole number, so therefore the ones around 375 would be the closest whole numbers.
Now, 400 is one of the easier to remember square numbers. It is 20 squared. 375 is pretty close to 400, however its slightly lower. So now, let's look at the closest perfect square that's less than 400: 19^2, or 361.
375 is between 361 and 400, so therefore it is between the square root of 361 and 400, or 19 and 20.
Good luck!