Question

с решением плиз помогите срочно!!!

Answer 1

$\sqrt{5+2\sqrt{6} }+\sqrt{10-2\sqrt{21} }=\sqrt{3+2\sqrt{6}+2 }+\sqrt{7-2\sqrt{21}+3 }=\\\\=\sqrt{(\sqrt{3})^{2}+2\cdot\sqrt{3}\cdot\sqrt{2} +(\sqrt{2})^{2}} +\sqrt{(\sqrt{7})^{2}-2\cdot\sqrt{7}\cdot\sqrt{3} +(\sqrt{3})^{2}}=\\\\=\sqrt{(\sqrt{3} +\sqrt{2})^{2}} +\sqrt{(\sqrt{7} -\sqrt{3})^{2}} =|\sqrt{3} +\sqrt{2}|+|\sqrt{7} -\sqrt{3} |=\\\\=\sqrt{3}+\sqrt{2} +\sqrt{7} -\sqrt{3}=\boxed{\sqrt{2} +\sqrt{7}}$