Đáp án:
-1.5/ $\sqrt{(2+\sqrt2)^2}+\sqrt{11-6\sqrt2}$
$=|2+\sqrt2|+\sqrt{3^2-2.3\sqrt2+2}$
$=2+\sqrt2+\sqrt{(3-\sqrt2)^2}$
$=2+\sqrt2+|3-\sqrt2|$
$=2+\sqrt2+3-\sqrt2=5$
-1.6/ $\sqrt{(4-2\sqrt3)^2}-\sqrt{4+2\sqrt3}$
$=\sqrt{(3-2\sqrt3+1)^2}-\sqrt{3+2\sqrt3+1}$
$=|(\sqrt3-1)^2|-\sqrt{(\sqrt3+1)^2}$
$=(\sqrt3-1)^2-(\sqrt3+1)$
$=4-2\sqrt3-\sqrt3-1=3-3\sqrt3$
-1.7/ $\sqrt{10+2\sqrt{21}}-\sqrt{10-2\sqrt{21}}$
$=\sqrt{7+2\sqrt7\sqrt3+3}-\sqrt{7-2\sqrt7\sqrt3+3}$
$=\sqrt{(\sqrt7+\sqrt3)^2}-\sqrt{(\sqrt7-\sqrt3)^2}$
$=\sqrt7+\sqrt3-(\sqrt7-\sqrt3)$
$=\sqrt7+\sqrt3-\sqrt7+\sqrt3=2\sqrt3$
-1.8/ $\sqrt{8+2\sqrt{15}}-\sqrt{8-2\sqrt{15}}$
$=\sqrt{5+1\sqrt5\sqrt3+3}-\sqrt{5-1\sqrt5\sqrt3+3}$
$=\sqrt{(\sqrt5+\sqrt3)^2}-\sqrt{(\sqrt5-\sqrt3)^2}$
$=\sqrt5+\sqrt3-(\sqrt5-\sqrt3)$
$=\sqrt5+\sqrt3-\sqrt5+\sqrt3=2\sqrt3$
