Maharashtra BoardEnglish MediumSTD 8MathsCubes and Cube Roots2 Marks
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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