Hi! I'm happy to help!
A square root, means:
√x=y
This means that:
x=y·y=√x·√x
When we have the square button, it causes everything to be multiplied by itself once.
√x²=x
Due to the fact that the squared symbol is outside of the parenthesis, it causes both the square toot of 2, and the square root of 3, to be squared.
Now that we know this, √2², and √3²= 2, and 3.
This is why we get 2+3.
2+3=5, which is pretty self explanatory.
I hope this was helpful, keep learning! :D