Maharashtra BoardEnglish MediumSTD 8MathsCubes and Cube Roots3 Marks
Question
Evaluate:
$\sqrt[3]{100}\times\sqrt[3]{270}$
✓
Answer
100 and 270 are not perfect cubes; therefore, we use the following property:
$\sqrt[3]{\text{ab}}=\sqrt[3]{\text{a}}\times\sqrt[3]{\text{b}}$ for any two integers a and b.
$\therefore\sqrt[3]{100}\times\sqrt[3]{270}$
$=\sqrt[3]{{100}\times{270}}$
$=\sqrt[3]{(2\times2\times5\times5)\times (2\times3\times3\times3\times5)}$ (By prime factorisation)
$=\sqrt[3]{\{2\times2\times2\}\times\{3\times3\times3\}\times\{5\times5\times5\}}$
$=2\times3\times5$
$=30$
Thus, the answer is 30.
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