Show that: [3] 27 [3] 64 = [3] 27 64 - Vidyadip

Question

Show that: $\sqrt[3]{27}\times\sqrt[3]{64}=\sqrt[3]{27\times64}$

✓

Answer

$\text{L.H.S}=\sqrt[3]{27}\times\sqrt[3]{64}$
$\sqrt[3]{27\times64}$
$=\sqrt[3]{3\times3\times3}\times\sqrt[3]{4\times4\times4}$
$=3\times4=12$
$\text{R.H.S}=\sqrt[3]{27}\times\sqrt[3]{64}$
$=\sqrt[3]{3\times3\times3\times4\times4\times4}$
$=\sqrt[3]{\{3\times3\times3\times\}\{4\times4\times4\}}$
$=3\times4=12$ Because $LHS$ is equal to $RHS,$ the equation is true.

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