$$\left[ {\frac{{8{{\left( {3.75} \right)}^3} + 1}}{{{{\left( {7.5} \right)}^2} - 6.5}}} \right]$$   is equal to :

Solution(By Examveda Team)

Given expression :
$$\eqalign{ & \left[ {\frac{{8{{\left( {3.75} \right)}^3} + 1}}{{{{\left( {7.5} \right)}^2} - 6.5}}} \right] \cr & = \frac{{{{\left( {2 \times 3.75} \right)}^3} + {1^3}}}{{{{\left( {7.5} \right)}^2} - \left( {7.5 \times 1} \right) + {1^2}}} \cr & = \frac{{{{\left( {7.5} \right)}^3} + {1^3}}}{{{{\left( {7.5} \right)}^2} - \left( {7.5 \times 1} \right) + {1^2}}} \cr & = \left( {\frac{{{a^3} + {b^3}}}{{{a^2} - ab + {b^2}}}} \right) \cr & = \frac{{\left( {a + b} \right)\left( {{a^2} - ab + {b^2}} \right)}}{{\left( {{a^2} - ab + {b^2}} \right)}} \cr & = \left( {a + b} \right) \cr & = \left( {7.5 + 1} \right) \cr & = 8.5 \cr} $$