Tính: a) \(\sqrt {12} .\left( {\sqrt {12} + \sqrt 3 } \right);\) b) \(\sqrt 8 .\left( {\sqrt {50} - \sqrt 2 } \right);\) c) \[{\left( {\sqrt 3 + \sqrt 2 } \right)^2} - 2\sqrt 6 .\]
Giải thích
a) \(\sqrt {12} .\left( {\sqrt {12} + \sqrt 3 } \right) = \sqrt {12} .\sqrt {12} + \sqrt {12} .\sqrt 3 \)
\( = \sqrt {{{12}^2}} + \sqrt {36} = 12 + 6 = 18.\)
b) \(\sqrt 8 .\left( {\sqrt {50} - \sqrt 2 } \right) = \sqrt 8 .\sqrt {50} - \sqrt 8 .\sqrt 2 \)
\( = \sqrt {400} - \sqrt {16} = 20 - 4 = 16.\)
c) \[{\left( {\sqrt 3 + \sqrt 2 } \right)^2} - 2\sqrt 6 \]
\[ = {\left( {\sqrt 3 } \right)^2} + {\left( {\sqrt 2 } \right)^2} + 2\sqrt 3 .\sqrt 2 - 2\sqrt 6 = 3 + 2 = 5.\]