Question
Examine whether the following numbers are rational or irrational.
$\sqrt[3]{5}\times\sqrt[3]{25}$
$\sqrt[3]{5}\times\sqrt[3]{25}$
✓
Answer
$\sqrt[3]{5}\times\sqrt[3]{25}$
$=\sqrt[3]{5\times25}$
$=\sqrt[3]{125}$
$=5,$ which is an integer
Hence, $\sqrt[3]{5}\times\sqrt[3]{25}$ is rational.
$=\sqrt[3]{5\times25}$
$=\sqrt[3]{125}$
$=5,$ which is an integer
Hence, $\sqrt[3]{5}\times\sqrt[3]{25}$ is rational.
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