Question
Show that: $\sqrt[3]{64}\times\sqrt[3]{729}=\sqrt[3]{64\times729}$
✓
Answer
$\text{L.H.S}=\sqrt[3]{64\times729}$
$=\sqrt[3]{4\times4\times4\times9\times9\times9}$
$=\sqrt[3]{\{4\times4\times4\}\times\{9\times9\times9\}}$
$=4\times9=36$
$\text{R.H.S}=\sqrt[3]{64}\times\sqrt[3]{729}$
$=\sqrt[3]{4\times4\times4}\times\sqrt[3]{9\times9\times9}$
$=4\times9=36$ Because $LHS$ is equal to $RHS,$ the equation is true.
$=\sqrt[3]{4\times4\times4\times9\times9\times9}$
$=\sqrt[3]{\{4\times4\times4\}\times\{9\times9\times9\}}$
$=4\times9=36$
$\text{R.H.S}=\sqrt[3]{64}\times\sqrt[3]{729}$
$=\sqrt[3]{4\times4\times4}\times\sqrt[3]{9\times9\times9}$
$=4\times9=36$ Because $LHS$ is equal to $RHS,$ the equation is true.
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