# Question #9a91c

Nov 19, 2017

$6 \left(3 + \sqrt{5}\right)$

#### Explanation:

If the question is:- ${\left(\sqrt{3} + \sqrt{15}\right)}^{2} t h e n :$

$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$\sqrt{3} + \sqrt{15}$
$\textcolor{w h i t e}{a a a a a a a a a a a}$$\times \underline{\sqrt{3} + \sqrt{15}}$
$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$3 + \sqrt{3} \cdot \sqrt{15}$
$\textcolor{w h i t e}{a a a a a a a a a a a a a a a a}$$+ \sqrt{3} \cdot \sqrt{15} + 15$
$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$\overline{3 + 2 \sqrt{3} \cdot \sqrt{15} + 15}$

$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$\therefore = 18 + 2 \sqrt{3} \cdot \sqrt{15}$

$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$\therefore 18 + 2 \sqrt{45}$

$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$\therefore = 18 + 2 \sqrt{5 \cdot 3 \cdot 3}$

$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$\sqrt{3} \cdot \sqrt{3} = 3$

$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$\therefore = 18 + 2 \cdot 3 \sqrt{5}$

$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$\therefore = 18 + 6 \sqrt{5}$

$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$\therefore = 6 \left(3 + \sqrt{5}\right)$