Evaluate [3] 216 343 - Vidyadip

Question

Evaluate $\sqrt[3]{216\times343}$

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Answer

By prime factorisation method
$\sqrt[3]{216\times343}$
$=\sqrt[3]{216}\times\sqrt[3]{343}$
$=\sqrt[3]{2\times2\times2\times3\times3\times3}\times\sqrt[3]{7\times7\times7}$
$=\sqrt[3]{(2)^3\times(3)^3}\times\sqrt[3]{(7)^3}$
$\sqrt[3]{216\times343}=(2)\times(3)\times(7)$
$\sqrt[3]{216\times343}=42$
$\therefore\sqrt[3]{216\times343}=42$

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