Binomial theorem expansion

Question

Obtain the first four terms of the expansion of $(1+8x)^{\frac{1}{2}}$ in ascending powers of $x$. By putting $x=\frac{1}{100}$, obtain the value of $\sqrt{3}$, correct to five decimal places.

Answer 1

When you expand it and substitute $x =1/100,$ you get an approximation to $\sqrt{1.08}.$ For the remainder of the question, note that $$ \frac{\sqrt{1.08}}{\sqrt3} =\sqrt{\frac{1.08}{3}}=\sqrt{.36}=.6 $$