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Cubes and Cube Roots — Maths STD 8 — Question

Maharashtra BoardEnglish MediumSTD 8MathsCubes and Cube Roots2 Marks
Question
Show that:
$\frac{\sqrt[3]{729}}{\sqrt[3]{1000}}=\frac{\sqrt[3]{729}}{\sqrt[3]{1000}}$
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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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