Thực hiện phép tính: a) 2 căn 50 - 3 căn 72 + 5 căn 32 . b) căn 2 + căn 162 - căn 200 + 2 căn 98

a) \[2\sqrt {50} - 3\sqrt {72} + 5\sqrt {32} \]

\[ = 10\sqrt 2 - 18\sqrt 2 + 20\sqrt 2 \]

\[ = 12\sqrt 2 \].

b) \(\sqrt 2 + \sqrt {162} - \sqrt {200} + 2\sqrt {98} \)

\( = \sqrt 2 + 9\sqrt 2 - 10\sqrt 2 + 14\sqrt 2 \)

\( = 14\sqrt 2 \).

c) \(\sqrt {{{\left( {3 - \sqrt 3 } \right)}^2}} + \sqrt {4 + 2\sqrt 3 } \)

\( = \left| {3 - \sqrt 3 } \right| + \sqrt {{{\left( {\sqrt 3 + 1} \right)}^2}} \)

\( = 3 - \sqrt 3 + \left| {\sqrt 3 + 1} \right|\)

\( = 3 - \sqrt 3 + \sqrt 3 + 1 = 4\).

d) \[\frac{1}{3}\sqrt {72} - 3\sqrt {50} - \frac{{\sqrt {66} }}{{\sqrt {33} }}\]

\[ = \frac{1}{3}.6\sqrt 2 - 3.5\sqrt 2 - \sqrt 2 \]

\[ = 2\sqrt 2 - 15\sqrt 2 - \sqrt 2 \]

\[ = - 14\sqrt 2 \].

e) \[\left( {3 - \frac{{5 + \sqrt {15} }}{{\sqrt 5 + \sqrt 3 }}} \right)\left( {3 + \frac{{5 - \sqrt 5 }}{{\sqrt 5 - 1}}} \right)\]

\[\left[ {3 - \frac{{\sqrt 5 \left( {\sqrt 5 + \sqrt 3 } \right)}}{{\sqrt 5 + \sqrt 3 }}} \right]\left[ {3 + \frac{{\sqrt 5 \left( {\sqrt 5 - 1} \right)}}{{\sqrt 5 - 1}}} \right]\]

\[ = \left( {3 - \sqrt 5 } \right)\left( {3 + \sqrt 5 } \right)\]

\[ = {\left( 3 \right)^2} - {\left( {\sqrt 5 } \right)^2}\]

\[ = 9 - 5 = 4\].

f) \(\frac{{5 + \sqrt {10} }}{{\sqrt 5 + \sqrt 2 }} + \frac{4}{{1 - \sqrt 5 }}\)

      \( = \frac{{\sqrt 5 \left( {\sqrt 5 + \sqrt 2 } \right)}}{{\sqrt 5 + \sqrt 2 }} + \frac{{4\left( {1 + \sqrt 5 } \right)}}{{\left( {1 - \sqrt 5 } \right)\left( {1 + \sqrt 5 } \right)}}\)

      \( = \sqrt 5 + \frac{{4\left( {1 + \sqrt 5 } \right)}}{{1 - 5}}\)

      \( = \sqrt 5 - \left( {1 + \sqrt 5 } \right)\)

      \( = \sqrt 5 - 1 - \sqrt 5 = - 1\).