$\begin{array}{l}
\dfrac{{\left( {\sqrt {10}  + \sqrt 6 } \right)\left( {\sqrt {4 - \sqrt {15} } } \right)}}{{8 - 2\sqrt {15} }} - \sqrt {15} \\
 = \dfrac{{\sqrt 2 \left( {\sqrt 5  + \sqrt 3 } \right)\sqrt {4 - \sqrt {3.5} } }}{{{{\left( {\sqrt 5  - \sqrt 3 } \right)}^2}}} - \sqrt {15} \\
 = \dfrac{{\sqrt {8 - 2\sqrt {3.5} } \left( {\sqrt 5  + \sqrt 3 } \right)}}{{{{\left( {\sqrt 5  - \sqrt 3 } \right)}^2}}} - \sqrt {15} \\
 = \dfrac{{\sqrt {{{\left( {\sqrt 5  - \sqrt 3 } \right)}^2}} \left( {\sqrt 5  + \sqrt 3 } \right)}}{{{{\left( {\sqrt 5  - \sqrt 3 } \right)}^2}}} - \sqrt {15} \\
 = \dfrac{{\sqrt 5  + \sqrt 3 }}{{\sqrt 5  - \sqrt 3 }} - \sqrt {15}  = \dfrac{{\left( {\sqrt 5  + \sqrt 3 } \right)\left( {\sqrt 5  + \sqrt 3 } \right)}}{{5 - 3}} - \sqrt {15} \\
 = \dfrac{{8 + 2\sqrt {15} }}{2} - \sqrt {15}  = 4 + \sqrt {15}  - \sqrt {15}  = 4
\end{array}$

Đáp án:

`B=4.` 

Giải thích các bước giải:

`B=((sqrt(10)+sqrt6)(sqrt{4-sqrt(15)}))/(8-2sqrt(15))-sqrt(15)`

`=((sqrt2(sqrt5+sqrt3))(sqrt{4-sqrt(15)}))/(5-2sqrt5sqrt3+3)-sqrt(15)`

`=((sqrt5+sqrt3)sqrt{8-2sqrt15})/(sqrt5-sqrt3)^2-sqrt(15)`

`=((sqrt5+sqrt3)(sqrt5-sqrt3))/(sqrt5-sqrt3)^2-sqrt(15)`

`=(sqrt5+sqrt3)/(sqrt5-sqrt3)-sqrt(15)`

`=((sqrt5+sqrt3)(sqrt5+sqrt3))/(5-3)-sqrt(15)`

`=((sqrt5+sqrt3)^2)/2-sqrt(15)`

`=(8+2sqrt(15))/2-sqrt(15)`

`=4+sqrt(15)-sqrt(15)=4`

Vậy `B=4.`