Question

x_2=1/2(x_1+n/x_1) ; let x_1= 3/2

Rational approximations to square roots can be found using a formula discovered by the ancient bablonians. Let x_1 be the first rational approximation for sqrt(n).

Answer 1

Then x_2 will be a better approximation for sqrt(n), and we can repeat the computation with x_2 replacing x_1. Starting with x_1, find the next two rational approximations for sqrt(2)

Answer 2

\[x_2=1/2(x_1+n/x_1)\]