# Question #fe9b0

Apr 3, 2017

See below:

#### Explanation:

If the question is:

${\left(\sqrt{5} - 6\right)}^{2}$

Then you can rewrite this as:

$\left(\sqrt{5} - 6\right) \left(\sqrt{5} - 6\right)$

To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

$\left(\textcolor{red}{\sqrt{5}} - \textcolor{red}{6}\right) \left(\textcolor{b l u e}{\sqrt{5}} - \textcolor{b l u e}{6}\right)$ becomes:

$\left(\textcolor{red}{\sqrt{5}} \times \textcolor{b l u e}{\sqrt{5}}\right) - \left(\textcolor{red}{\sqrt{5}} \times \textcolor{b l u e}{6}\right) - \left(\textcolor{red}{6} \times \textcolor{b l u e}{\sqrt{5}}\right) + \left(\textcolor{red}{6} \times \textcolor{b l u e}{6}\right)$

$5 - 6 \sqrt{5} - 6 \sqrt{5} + 36$

We can now combine like terms:

$5 + 36 + \left(- 6 - 6\right) \sqrt{5}$

$41 - 12 \sqrt{5}$

If you want this as a single number, $\sqrt{5} = 2.236$ rounded to the nearest thousandth.

Substituting this in gives:

$41 - \left(12 \times 2.236\right)$

$41 - 26.833$

$14.167$ rounded to the nearest thousandth.