Gujarat BoardEnglish MediumSTD 8MATHSCubes and Cube Roots2 Marks
Question
Show that: $\frac{\sqrt[3]{729}}{\sqrt[3]{1000}}=\frac{\sqrt[3]{729}}{\sqrt[3]{1000}}$
✓
Answer
$\text{LHS}=\frac{\sqrt[3]{729}}{\sqrt[3]{1000}}$
$=\frac{\sqrt[3]{9\times9\times9}}{\sqrt[3]{10\times10\times10}}$
$=\frac{9}{10}$
$\text{RHS}=\sqrt[3]\frac{{729}}{{1000}}$
$=\sqrt[3]\frac{{9\times9\times9}}{{10\times10\times10}}$
$=\sqrt[3]{\frac{9}{10}\times\frac{9}{10}\times\frac{9}{10}}$
$=\sqrt[3]{(\frac{9}{10})^3}$
$=\frac{9}{10}$ Because $LHS$ is equal to $RHS$, the equation is true.
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