a) \(\eqalign{& \sqrt {{{\left( {2 - \sqrt 3 } \right)}^2}} + \sqrt {4 - 2\sqrt 3 } \cr & = \left| {2 - \sqrt 3 } \right| + \sqrt {3 - 2\sqrt 3 + 1} \cr} \)\(\eqalign{& = 2 - \sqrt 3 + \sqrt {{{\left( {\sqrt 3 - 1} \right)}^2}} \cr & = 2 - \sqrt 3 + \left| {\sqrt 3 - 1} \right| \cr} \)\( = 2 - \sqrt 3 + \sqrt 3 - 1 = 1\)
b) \(\eqalign{& \sqrt {15 - 6\sqrt 6 } + \sqrt {33 - 12\sqrt 6 } \cr & = \sqrt {9 - 2.3\sqrt 6 + 6} + \sqrt {9 - 2.3.2\sqrt 6 + 24} \cr} \)\(\eqalign{
& = \sqrt {{{\left( {3 - \sqrt 6 } \right)}^2}} + \sqrt {{{\left( {3 - 2\sqrt 6 } \right)}^2}} \cr
& = \left| {3 - \sqrt 6 } \right| + \left| {3 - 2\sqrt 6 } \right| \cr} \)\( = 3 - \sqrt 6 + 2\sqrt 6 - 3 = \sqrt 6 \)
c) \(\eqalign{& \left( {15\sqrt {200} - 3\sqrt {450} + 2\sqrt {50} } \right):\sqrt {10} \cr & = 15\sqrt {{{200} \over {10}}} - 3\sqrt {{{450} \over {10}}} + 2\sqrt {{{50} \over {10}}} \cr} \)\(\eqalign{& = 15\sqrt {20} - 3\sqrt {45} + 2\sqrt 5 \cr & = 15\sqrt {4.5} - 3\sqrt {9.5} + 2\sqrt 5 \cr} \)\(\eqalign{& = 15.2\sqrt 5 - 3.3\sqrt 5 + 2\sqrt 5 \cr & = 30\sqrt 5 - 9\sqrt 5 + 2\sqrt 5 = 23\sqrt 5 \cr} \)
