Tính giá trị của các biểu thức sau:

a) \(3\sqrt {45} + \frac{{5\sqrt {15} }}{{\sqrt 3 }} - 2\sqrt {245} ;\)

b) \[\frac{{\sqrt {12} - \sqrt 4 }}{{\sqrt 3 - 1}} - \frac{{\sqrt {21} + \sqrt 7 }}{{\sqrt 3 + 1}} + \sqrt 7 ;\]

c) \(\frac{{3 - \sqrt 3 }}{{1 - \sqrt 3 }} + \sqrt 3 \left( {2\sqrt 3 - 1} \right) + \sqrt {12} ;\)

d) \(\frac{{\sqrt 3 - 1}}{{\sqrt 2 }} + \frac{{\sqrt 2 }}{{\sqrt 3 - 1}} - \frac{6}{{\sqrt 6 }}.\)

a) \(3\sqrt {45} + \frac{{5\sqrt {15} }}{{\sqrt 3 }} - 2\sqrt {245} \)

\( = 3\sqrt {9.5} + 5\sqrt {\frac{{15}}{3}} - 2\sqrt {49.5} \)

\( = 9\sqrt 5 + 5\sqrt 5 - 14\sqrt 5 = 0.\)

b) \[\frac{{\sqrt {12} - \sqrt 4 }}{{\sqrt 3 - 1}} - \frac{{\sqrt {21} + \sqrt 7 }}{{\sqrt 3 + 1}} + \sqrt 7 \]

\[ = \frac{{\sqrt 4 \left( {\sqrt 3 - 1} \right)}}{{\sqrt 3 - 1}} - \frac{{\sqrt 7 \left( {\sqrt 3 + 1} \right)}}{{\sqrt 3 + 1}} + \sqrt 7 \]

\( = \sqrt 4 - \sqrt 7 + \sqrt 7 = 2.\)

c) \(\frac{{3 - \sqrt 3 }}{{1 - \sqrt 3 }} + \sqrt 3 \left( {2\sqrt 3 - 1} \right) + \sqrt {12} \)

\( = \frac{{\sqrt 3 \left( {\sqrt 3 - 1} \right)}}{{1 - \sqrt 3 }} + 3.2 - \sqrt 3 + 2\sqrt 3 \)

\( = - \sqrt 3 + 6 - \sqrt 3 + 2\sqrt 3 = 6.\)

d) \(\frac{{\sqrt 3 - 1}}{{\sqrt 2 }} + \frac{{\sqrt 2 }}{{\sqrt 3 - 1}} - \frac{6}{{\sqrt 6 }}\)

\( = \frac{{\left( {\sqrt 3 - 1} \right)\sqrt 2 }}{{\sqrt 2 .\sqrt 2 }} + \frac{{\sqrt 2 \left( {\sqrt 3 + 1} \right)}}{{\left( {\sqrt 3 - 1} \right)\left( {\sqrt 3 + 1} \right)}} - \sqrt 6 \)

\[ = \frac{{\sqrt 6 - \sqrt 2 }}{2} + \frac{{\sqrt 6 + \sqrt 2 }}{{{{\left( {\sqrt 3 } \right)}^2} - {1^2}}} - \sqrt 6 \]

\[ = \frac{{\sqrt 6 - \sqrt 2 }}{2} + \frac{{\sqrt 6 + \sqrt 2 }}{2} - \sqrt 6 \]

\( = \frac{{\sqrt 6 - \sqrt 2 + \sqrt 6 + \sqrt 2 - 2\sqrt 6 }}{2} = 0.\)