Aptitude Question ID: 107135

Find the value of :
$(\sqrt[3]{3.5}+\sqrt[3]{2.5})\left \{ (\sqrt[3]{3.5})^{2}-\sqrt[3]{8.75}+(\sqrt[3]{2.5})^{2} \right \}$
[A]1
[B]5
[C]5.375
[D]6

6
Given Expression, $(\sqrt[3]{3.5}+\sqrt[3]{2.5})\left \{ (\sqrt[3]{3.5})^{2}-\sqrt[3]{8.75}+(\sqrt[3]{2.5})^{2} \right \}$
Here let $\sqrt[3]{3.5} = a$ and $\sqrt[3]{2.5} = b$
$\because (a+b)(a^{2}-ab+b^{2}) = a^{3}+b^{3}$
$\therefore (\sqrt[3]{3.5}+\sqrt[3]{2.5})\left \{ (\sqrt[3]{3.5})^{2}-\sqrt[3]{8.75}+(\sqrt[3]{2.5})^{2} \right \} = \left ( \sqrt[3]{3.5} \right )^{3} + \left ( \sqrt[3]{2.5} \right )^{3}$
$= 3.5+2.5 = 6$
Hence option [D] is correct answer.