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 $30.$
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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