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.

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