# How do you estimate sqrt14.5?

Feb 19, 2017

$\sqrt{14.5} \approx 3.8$

#### Explanation:

${3}^{2} = 9 < 14.5 < 16 = {4}^{2}$

So $\sqrt{14.5}$ is somewhere between $3$ and $4$.

To be more specific we can linearly interpolate - approximating the section of the parabola $y = {x}^{2}$ between $\left(3 , 9\right)$ and $\left(4 , 16\right)$ using a straight line...

$\frac{14.5 - 9}{16 - 9} = \frac{5.5}{7} = 0.7 \overline{857142} \approx 0.8$

So $\sqrt{14.5} \approx 3 + 0.8 = 3.8$