# How do you order the following from least to greatest -11/5, -pi, -2.98, -sqrt7?

Feb 5, 2017

$- \pi , - 2.98 , - \sqrt{7} , - \frac{11}{5}$

#### Explanation:

Given:

$- \frac{11}{5} , - \pi , - 2.98 , - \sqrt{7}$

Let's get a decimal approximation for $\sqrt{7}$ first:

Note that ${2}^{2} = 4 < 7 < 9 = {3}^{2}$

So choose $\frac{5}{2}$ as a first approximation.

Then applying one step of Newton's method, a better approximation is:

$\frac{{5}^{2} + 7 \cdot {2}^{2}}{2 \cdot 5 \cdot 2} = \frac{25 + 28}{20} = \frac{53}{20} = 2.65$

So we have:

$\left\{\begin{matrix}- \frac{11}{5} = - 2.2 \\ - \pi \approx - 3.14 \\ - 2.98 = - 2.98 \\ - \sqrt{7} \approx - 2.65\end{matrix}\right.$

So in ascending order:

$- \pi , - 2.98 , - \sqrt{7} , - \frac{11}{5}$