Maharashtra BoardEnglish MediumSTD 8MathsCubes and Cube Roots2 Marks
Question
Show that:
$\sqrt[3]{-125-1000}=\sqrt[3]{-125}\times\sqrt[3]{-1000}$
✓
Answer
$\text{L.H.S}=\sqrt[3]{-125\times-1000}$
$=\sqrt[3]{-5\times-5\times-5\times-10\times-10\times-10}$
$=\sqrt[3]{\{-5\times-5\times-5\times\}\times\{-10\times-10\times-10\}}$
$=-5\times-10=-50$
$\text{R.H.S}=\sqrt[3]{-125}\times\sqrt[3]{-1000}$
$=\sqrt[3]{-5\times-5\times-5}\times\sqrt[3]{{\{-10\times-10\times-10\}}}$
$=-5\times-10=50$
Because LHS is equal to RHS, the equation is true.
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