(1)
The square root of 8 is somewhere between 2 and 3, because

So,
is between -1 and 0, whereas
is between 2 and 3.
So, we have

(2)
The square root of 25 is 5, because 
So, the left hand side is exactly

You seem to have already computed the right hand side to be 2.30, so we have
