Tính giá trị biểu thức: A = \(\left( {4 + \sqrt {15} } \right)\left( {\sqrt {10} - \sqrt 6 } \right)\sqrt {4 - \sqrt {15} } \).

\(\left( {4 + \sqrt {15} } \right)\left( {\sqrt {10} - \sqrt 6 } \right)\sqrt {4 - \sqrt {15} } \)

= \(\sqrt {4 + \sqrt {15} } .\sqrt 2 \left( {\sqrt 5 - \sqrt 3 } \right)\sqrt {\left( {4 - \sqrt {15} } \right)\left( {\sqrt {4 + \sqrt {15} } } \right)} \)

= \(\sqrt {8 + 2\sqrt {15} } .\left( {\sqrt 5 - \sqrt 3 } \right).\sqrt {16 - 15} \)

= \(\sqrt {{{\left( {\sqrt 3 } \right)}^2} + 2.\sqrt 3 .\sqrt 5 + {{\left( {\sqrt 5 } \right)}^2}} .\left( {\sqrt 5 - \sqrt 3 } \right).1\)

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

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

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

= 5 – 3

= 2.

Vậy A = 2.