# (2root5+3root2)square ?

Jun 22, 2018

$38 + 12 \sqrt{10}$

#### Explanation:

To format this write:

hash ( 2sqrt(5)+3sqrt(2) )^2 hash

${\left(2 \sqrt{5} + 3 \sqrt{2}\right)}^{2}$

Write as:

color( blue)((2sqrt(5)+3sqrt(2))color(green)(( 2sqrt(5)+3sqrt(2))

Multiply everything inside the green bracket by everything in the blue.

$\textcolor{g r e e n}{\textcolor{b l u e}{2 \sqrt{5}} \left[\textcolor{w h i t e}{\frac{.}{.}} 2 \sqrt{5} + 3 \sqrt{2} \textcolor{w h i t e}{\frac{.}{.}}\right] \textcolor{w h i t e}{\text{ddddd}} \textcolor{b l u e}{+ 3 \sqrt{2}} \left[\textcolor{w h i t e}{\frac{.}{.}} 2 \sqrt{5} + 3 \sqrt{2} \textcolor{w h i t e}{\frac{.}{.}}\right]}$

Notice the + followed the $\textcolor{b l u e}{+ 3 \sqrt{2}}$

${\left(2 \sqrt{5}\right)}^{2} + 2 \sqrt{5} \times 3 \sqrt{2} \textcolor{w h i t e}{\text{dddd}} + 2 \sqrt{5} \times 3 \sqrt{2} + {\left(3 \sqrt{2}\right)}^{2}$

Lets introduce a pairs of bracket to group things.

$\left[{\left(2 \sqrt{5}\right)}^{2}\right] + \left[\textcolor{w h i t e}{\frac{2}{2}} 2 \sqrt{5} \times 3 \sqrt{2} \textcolor{w h i t e}{\text{dddd") +2sqrt(5) xx3sqrt(2) color(white)("d}}\right] + \left[{\left(3 \sqrt{2}\right)}^{2}\right]$

We can factor out the $2 \sqrt{5}$

$\left[4 \times 5\right] \textcolor{w h i t e}{\text{ddd")+ color(white)("dd")2 sqrt(5)[ color(white)(2/2)3sqrt(2) color(white)("dddd") +3sqrt(2) color(white)("d")] color(white)("ddddd}} + \left[9 \times 2\right]$

$\textcolor{w h i t e}{\text{dd")20 color(white)("dddd")+ color(white)("ddddddddd")[2sqrt5 xx 6sqrt2] color(white)("ddddddddd}} + 18$

$\textcolor{w h i t e}{\text{d}}$
$\textcolor{w h i t e}{\text{d}}$

$\textcolor{w h i t e}{\text{dddddddddddddddddd}} 20 + 18 + 12 \sqrt{5 \times 2}$

$\textcolor{w h i t e}{\text{dddddddddddddddddddd}} 38 + 12 \sqrt{10}$