If the expansion is of other forms, can try the method shown in example 2.
How do you select a suitable value for the approximation?
Make sure the value selected is within the range of values for which the expansion is valid. In this example, the valid range is from -4 to 4.
4-x = (13 / perfect square) or (perfect square/13)
So 4-x = (13 /4 or 13/9) or (49/13)
x= 3/13 or 3/4 or 23/9
Choose the smallest value 3/13 as value closer to 0 gives better approximation.