Question

sqrt{19-8sqrt{3}}+3sqrt{3}

Answer 1

$sqrt{19-8sqrt{3}}+3sqrt{3}=sqrt{16-8sqrt{3}+3}+3sqrt{3}=$

$=sqrt{(4-sqrt{3})^2}+3sqrt{3}=|4-sqrt{3}|+3sqrt{3}=4-sqrt{3}+3sqrt{3}=$

$=4+2sqrt{3}=2(2+sqrt{3})$