căn bậc hai(19-6căn bậc hai(3)) căn bậc hai(21+12căn bậc hai(3)) căn bậc hai(57-40căn bậc hai(2)) căn bậc hai(79+20căn bậc hai(3)) căn bậc hai(16+6căn

$\sqrt{19-6\sqrt{2}}=\sqrt{18-6\sqrt{2}-1}=\sqrt{(3\sqrt{2})^2-2.3\sqrt{2}.1+1^2}=\sqrt{(3\sqrt{2}-1)^2}\\=|3\sqrt{2}-1|=3\sqrt{2}-1$

$\sqrt{21+12\sqrt{3}}=\sqrt{9+12\sqrt{3}+12}=\sqrt{3^2+2.3.2\sqrt{3}+(2\sqrt{3})^2}=\sqrt{(3+2\sqrt{3})^2}\\=|3+2\sqrt{3}|=3+2\sqrt{3}$

$\sqrt{47-40\sqrt{2}}=\sqrt{32-40\sqrt{2}+25}=\sqrt{(4\sqrt{2})^2-2.4\sqrt{2}.5+5^2}=\sqrt{(4\sqrt{2}-5)^2}\\=|4\sqrt{2}-5|=4\sqrt{2}-5$

$\sqrt{79+20\sqrt{3}}=\sqrt{75+20\sqrt{3}+4}=\sqrt{(5\sqrt{3})^2+2.5\sqrt{3}.2+2^2}=\sqrt{(5\sqrt{3}+2)^2}\\=|5\sqrt{3}+2|=5\sqrt{3}+2$

$\sqrt{16+6\sqrt{7}}=\sqrt{9+6\sqrt{7}+7}=\sqrt{3^2+2.3.\sqrt{7}+(\sqrt{7})^2}=\sqrt{(3+\sqrt{7})^2}\\=|3+\sqrt{7}|=3+\sqrt{7}$