`17. sqrt(14-6 sqrt 5) + sqrt(14 + 6 sqrt 5)`
`= sqrt (9 - 2 . sqrt 9 . sqrt 5 + 5) + sqrt(9 + 2 . sqrt 9 + sqrt 5 + 5)`
`= sqrt(3-sqrt5)^2 + sqrt(3+sqrt5)^2`
`= 3 - sqrt 5 + 3 + sqrt 5`
`= 6`
18) \(\sqrt{7-2\sqrt{10}}-\sqrt{7+2\sqrt{10}}\)
\(=\sqrt{5-2\sqrt{5.2}+2}-\sqrt{5+2\sqrt{5.2}+2}\\ =\sqrt{\left(\sqrt{5}-\sqrt{2}\right)^2}-\sqrt{\left(\sqrt{5}+\sqrt{2}\right)^2}\\ =\left|\sqrt{5}-\sqrt{2}\right|-\left|\sqrt{5}+\sqrt{2}\right|\\ =\sqrt{5}-\sqrt{2}-\sqrt{5}-\sqrt{2}=-2\sqrt{2}\)
19) \(\sqrt{15-6\sqrt{6}}+\sqrt{35-12\sqrt{6}}\)
\(=\sqrt{9-2.3.\sqrt{6}+6}+\sqrt{24-2.2\sqrt{6}.3+9}\\ =\sqrt{\left(3-\sqrt{6}\right)^2}+\sqrt{\left(2\sqrt{6}-3\right)^2}\\ =\left|3-\sqrt{6}\right|+\left|2\sqrt{6}-3\right|\\ =3-\sqrt{6}+2\sqrt{6}-3=\sqrt{6}\)
20) \(\sqrt{5-2\sqrt{6}}-\sqrt{5+2\sqrt{6}}\)
\(=\sqrt{3-2\sqrt{3.2}+2}-\sqrt{3+2\sqrt{3.2}+2}\\ =\sqrt{\left(\sqrt{3}-\sqrt{2}\right)^2}-\sqrt{\left(\sqrt{3}+\sqrt{2}\right)^2}\\ =\left|\sqrt{3}-\sqrt{2}\right|-\left|\sqrt{3}+\sqrt{2}\right|\\ =\sqrt{3}-\sqrt{2}-\sqrt{3}-\sqrt{2}=-2\sqrt{2}\)
21) \(\sqrt{11-6\sqrt{2}}-\sqrt{3-2\sqrt{2}}\)
\(=\sqrt{9-2.3.\sqrt{2}+2}-\sqrt{2-2\sqrt{2}+1}\\ =\sqrt{\left(3-\sqrt{2}\right)^2}-\sqrt{\left(\sqrt{2}-1\right)^2}\\ =\left|3-\sqrt{2}\right|-\left|\sqrt{2}-1\right|\\ =3-\sqrt{2}-\sqrt{2}-1=2-2\sqrt{2}\)
23) \(\left(\sqrt{2}-3\right)\sqrt{11+6\sqrt{2}}\)
\(=\left(\sqrt{2}-3\right)\sqrt{9+2.3.\sqrt{2}+2}\\ =\left(\sqrt{2}-3\right)\sqrt{\left(3+\sqrt{2}\right)^2}\\ =\left(\sqrt{2}-3\right)\left(3+\sqrt{2}\right)\\ =2-9=-7\)
24) \(\left(\sqrt{3}+\sqrt{5}\right)\sqrt{7-2\sqrt{10}}\)
\(=\left(\sqrt{3}+\sqrt{5}\right)\sqrt{5-2\sqrt{5.2}+2}\\ =\left(\sqrt{3}+\sqrt{5}\right)\sqrt{\left(\sqrt{5}-\sqrt{2}\right)^2}\\ =\left(\sqrt{3}+\sqrt{5}\right)\left(\sqrt{5}-\sqrt{2}\right)\)
25) \(\left(\sqrt{7}-\sqrt{3}\right)\sqrt{10+2\sqrt{21}}\)
\(=\left(\sqrt{7}-\sqrt{3}\right)\sqrt{7+2.\sqrt{7.3}+3}\\ =\left(\sqrt{7}-\sqrt{3}\right)\sqrt{\left(\sqrt{7}+\sqrt{3}\right)^2}\\ =\left(\sqrt{7}-\sqrt{3}\right)\left(\sqrt{7}+\sqrt{3}\right)\\ =7-3=4\)
