Question

Engineers and physicists are fond of using the approximation Square root (1+x) = 1+(x/2)?

What approximation do you suppose the engineers and physicists would use for the quantity (1+x)^(3/2)

Answer 1

The approximation is only good when x is much less than 1.

It is obtained from the Taylor series rule

f(x) = f(0) + f'(0) * x

= 1 + (3/2)*(1+x)^(1/2)*x + ...
(evaluated at x=0)
= 1 + (3/2)x