a, $\sqrt{18-2\sqrt{17}}$
$=\sqrt{17-2.\sqrt{17}.\sqrt{1}+1}$
$=\sqrt{(\sqrt{17}-1)^2}$
$=|\sqrt{17}-1|$
$=\sqrt{17}-1$
b, $\sqrt{8+2\sqrt{7}}$
$=\sqrt{7+2\sqrt{7}.\sqrt{1}+1}$
$=\sqrt{(\sqrt{7}+1)^2}$
$=|\sqrt{7}+1|$
$=\sqrt{7}+1$
c, $\sqrt{38-2\sqrt{37}}$
$=\sqrt{37-2\sqrt{37}.\sqrt{1}+1}$
$=\sqrt{(\sqrt{37}-1)^2}$
$=|\sqrt{37}-1|$
$=\sqrt{37}-1$
d, $\sqrt{9-4\sqrt{5}}$
$=\sqrt{5-2.2.\sqrt{5}+4}$
$=\sqrt{(\sqrt{5}-2)^2}$
$=|\sqrt{5}-2|$
$=\sqrt{5}-2$
e, $\sqrt{11-6\sqrt{2}}$
$=\sqrt{9-2.3\sqrt{2}+2}$
$=\sqrt{(3-\sqrt{2})^2}$
$=|3-\sqrt{2}|$
$=3-\sqrt{2}$
f, $\sqrt{(5-\sqrt{2})^2}$
$=|5-\sqrt{2}|$
$=5-\sqrt{2}$
