Use this result to deduce a rational approximation to \(\sqrt 5 - \sqrt 3\).
Deduce, or obtain otherwise, a rational approximation to \(\sqrt 5 + \sqrt 3\).
Counting & Binomials
Question
If \(\dfrac{b}{a}\) is small enough for powers of \(\dfrac{b}{a}\) higher than the third to be neglected, show that
\[\begin{equation*}
(a+b)^\frac{1}{2} - (a-b)^\frac{1}{2} = a^\frac{1}{2} \left( \frac{b}{a} + \frac{b^3}{8a^3} \right).
\end{equation*}\]
