Using binomial expansion to evaluate $\sqrt{104}$

Question

Question:Use binomial expansion to evaluate $\sqrt{104}$

The answer should be $10.1980$

I understand that I have to get it to the form $(n+x)^{1/2}$ but I'm not sure how to.

I have completed a similar question but with $\sqrt{0.96}$, in which I worked out $x=-0.04$ and went on to show solution, but $x$ is not $103$ in this question.

Answer 1

By the binomial expansion, $\sqrt{1+h} \approx 1+\frac{h}{2}-\frac{h^2}{8}$ for small $h$. Therefore $$ \sqrt{104}=10\sqrt{1+0.04} \approx 1+\frac{0.04}{2}-\frac{0.04^2}{8} = 10.1980 $$