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You have,  \sqrt{6+2\sqrt{3}+2\sqrt{2}+2\sqrt{6}}
=  \sqrt{(\sqrt{3})^{2}+(\sqrt{2})^{2}+(\sqrt{1}^{2})+2(\sqrt{3}+\sqrt{2}+\sqrt{6})}
From the identity, a²+b²+c²+2(ab+bc+ca) = (a+b+c)², given number is, =  \sqrt{( \sqrt{3}+\sqrt{2}+1)^{2}} =  \sqrt{3} + \sqrt{2} +1.
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