Chapter 6.4, Problem 188E

In the following exercises, use the binomial approximation $\sqrt{1-x}\approx 1-\frac{x}{2}-\frac{x^2}{8}-\frac{x^3}{16}-\frac{5x^5}{128}-\frac{7x^5}{256}$ for |x| <1 to approximate each number. Compare this value to the value given by a scientific calculator.

188. [T] $\frac{1}{\sqrt{2}}$ using x = in (1 — x)1/2