Question

Without finding actual cubes, find ${\left(\frac{3}{4}\right)}^3+{\left(\frac{5}{8}\right)}^3+{\left(\frac{11}{8}\right)}^3$

Answer 1

$\frac{(3{)}^3}{(4{)}^3}+\frac{(5{)}^3}{(8{)}^3}+\frac{(11{)}^3}{(8{)}^3}$

$\Rightarrow \frac{(3{)}^3\times 8+(5{)}^3+(11{)}^3}{(8{)}^3}$

$=\frac{216+125+1331}{512}$

$=\frac{1672}{512}$

$=\frac{209}{64}$