Question
Show that:
$\sqrt[3]{-125\times216}=\sqrt[3]{-125}\times\sqrt[3]{216}$
$\sqrt[3]{-125\times216}=\sqrt[3]{-125}\times\sqrt[3]{216}$
✓
Answer
$\text{L.H.S}=\sqrt[3]{-125\times216}$
$=\sqrt[3]{-5\times-5\times-5\times\{2\times2\times2\times3\times3\times3}\}$
$=\sqrt[3]{\{-5\times-5\times-5\times\}\times\{2\times2\times2\}\times\{\times3\times3\times3}\}$
$=-5\times2\times3=-30$
$\text{R.H.S}=\sqrt[3]{-125}\times\sqrt[3]{216}$
$=\sqrt[3]{-5\times-5\times-5}\times\sqrt[3]{\{2\times2\times2\}\times{\{3\times3\times3\}}}$
$=-5\times(2\times3)=-30$
Because LHS is equal to RHS, the equation is true.
$=\sqrt[3]{-5\times-5\times-5\times\{2\times2\times2\times3\times3\times3}\}$
$=\sqrt[3]{\{-5\times-5\times-5\times\}\times\{2\times2\times2\}\times\{\times3\times3\times3}\}$
$=-5\times2\times3=-30$
$\text{R.H.S}=\sqrt[3]{-125}\times\sqrt[3]{216}$
$=\sqrt[3]{-5\times-5\times-5}\times\sqrt[3]{\{2\times2\times2\}\times{\{3\times3\times3\}}}$
$=-5\times(2\times3)=-30$
Because LHS is equal to RHS, the equation is true.
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