Rút gọn biểu thức sau

a) \(\sqrt {5 - 2\sqrt 6 } + \sqrt 2 \);

b) \(\sqrt {8 - 2\sqrt {15} } - \sqrt 5 \);

c) \(\sqrt {7 - 4\sqrt 3 } + 2\);

e) \(\sqrt {35 - 12\sqrt 6 } \);

g) \(\sqrt {7 - 3\sqrt 5 } \);

f) \(\sqrt {11 - 6\sqrt 2 } \).

a) \(\sqrt {5 - 2\sqrt 6 } + \sqrt 2 = \sqrt {3 - 2\sqrt 6 + 2} + \sqrt 2 = \sqrt {{{\left( {\sqrt 3 - \sqrt 2 } \right)}^2}} + \sqrt 2 = \sqrt 3 - \sqrt 2 + \sqrt 2 = \sqrt 3 \)

b) \(\sqrt {8 - 2\sqrt {15} } - \sqrt 5 = \sqrt {5 - 2\sqrt {15} + 3} - \sqrt 5 = \sqrt {{{(\sqrt 5 - \sqrt 3 )}^2}} - \sqrt 5 = \sqrt 5 - \sqrt 3 - \sqrt 5 = - \sqrt 3 \)

c) \(\sqrt {7 - 4\sqrt 3 } + 2 = \sqrt {4 - 4\sqrt 3 + 3} + 2 = \sqrt {{{(2 - \sqrt 3 )}^2}} + 2 = 2 - \sqrt 3 + 2 = 4 - \sqrt 3 \)

e) \(\sqrt {35 - 12\sqrt 6 } = \sqrt {27 - 12\sqrt 6 + 8} = \sqrt {{{(3\sqrt 3 - 2\sqrt 2 )}^2}} = 3\sqrt 3 - 2\sqrt 2 \)

g) \(\sqrt {7 - 3\sqrt 5 } = \sqrt {\frac{{14 + 6\sqrt 5 }}{2}} = \sqrt {\frac{{9 + 6\sqrt 5 + 5}}{2}} = \sqrt {\frac{{{{\left( {3 + \sqrt 5 } \right)}^2}}}{2}} = \frac{{3 + \sqrt 5 }}{{\sqrt 2 }}\)

f) \(\sqrt {11 - 6\sqrt 2 } = \sqrt {9 - 6\sqrt 2 + 2} = \sqrt {{{(3 - \sqrt 2 )}^2}} = 3 - \sqrt 2 \).