The Intermediate Value Theorem can be used to approximate a root. The following is an example of binary search in computer science. Suppose you want to approximate sqrt 2. You know that it is between 1 and 2. If you consider the function f(x)=x^2 -2, then note that f(1) is less than 0 and f(2) is greater than 0. Therefore by the Intermediate Value Theorem, there is a value, 1 is less than or equal to c and c is less than or equal to 2 such that f(C) = 0. Next choose the midpoint of these two values, 1.5, which is guaranteed to be within 0.5 of the actual root. f(1.5) will either be less than 0 or greater than 0. You can use the Intermediate Value Theorem again replacing 1.5 with the previous endpoint that has the same sign as 1.5. Continuing this process gives a sequence of approximations x subscript n with x subscript 1 =1.5. How many iterations must you do in order to be within 0.0078125 of the root?