Đáp án:
` 2`
Giải thích các bước giải:
$(4 + \sqrt {15} ).\left( {\sqrt {10} - \sqrt 6 } \right).\sqrt {4 - \sqrt {15} } \\
= \left( {4 + \sqrt {15} } \right).\left( {\sqrt 5 - \sqrt 3 } \right).\sqrt 2 .\sqrt {4 - \sqrt {15} } \\
= \left( {4 + \sqrt {15} } \right).\left( {\sqrt 5 - \sqrt 3 } \right).\sqrt {8 - 2\sqrt {15} } \\
= \left( {4 + \sqrt {15} } \right).\left( {\sqrt 5 - \sqrt 3 } \right).\sqrt {{{\left( {\sqrt 5 } \right)}^2} - 2.\sqrt 5 .\sqrt 3 + {{\left( {\sqrt 3 } \right)}^2}} \\
= \left( {4 + \sqrt {15} } \right).\left( {\sqrt 5 - \sqrt 3 } \right).\sqrt {{{\left( {\sqrt 5 - \sqrt 3 } \right)}^2}} \\
= \left( {4 + \sqrt {15} } \right).\left( {\sqrt 5 - \sqrt 3 } \right).\left| {\sqrt 5 - \sqrt 3 } \right|\\
= \left( {4 + \sqrt {15} } \right).{\left( {\sqrt 5 - \sqrt 3 } \right)^2}\\
= \left( {4 + \sqrt {15} } \right).\left( {8 - 2\sqrt {15} } \right)\\
= \left( {4 + \sqrt {15} } \right).\left( {4 - \sqrt {15} } \right).2\\
= \left( {{4^2} - 15} \right).2 = 2$
