The binomial expansion can in certain circumstances give highly accurate estimates of certain powers or roots. This can happen for example when we want to find not too high a power of a number that is close to an integer.
The binomial expansion is given by
Suppose we are asked to find
to 5 decimal places. We can substitute
and 
into the expression for the binomial expansion.
Further expansion is pointless since we only need 5 decimal places. After simplifying we have
to 5 decimal places.
Example: Find
to 10 decimal places. We can substitute
and 
into the expression for the binomial expansion.
Further expansion is pointless since we only need 10 decimal places.
We have
