Substitution in Binomial theorem

Question

By substituting $0.08$ for $x$ in $(1+x)^{1/2}$ and its expansion to find $\sqrt 3$, correct to four significant figure. The answer is $1.732$ given by the practice. I couldn't find the connection by substitution.

Answer 1

Hint:

$ \sum_{k=0}^2 {\frac{1}{2} \choose k}\cdot 0.08^k= \left(1\cdot 0.08^0 +\frac{0.5}{1}\cdot 0.08^1+\frac{0.5\cdot (-0.5)}{1\cdot 2}\cdot 0.08^2 \right) =1.732 \cdot \frac{3}{5}$