MCQ
The simplest rationalising factor $\sqrt[3]{500}$ is
- A$\sqrt{5}$
- B3
- C$\sqrt[3]{5}$
- ✓$\sqrt[3]{2}$
✓
Answer
Correct option: D.
$\sqrt[3]{2}$
(d)
We find that
$\sqrt[3]{500} \times \sqrt[3]{2}=\sqrt[3]{500 \times 2}=\sqrt[3]{10^3}=10$, which is a rational number.
Hence, $\sqrt[3]{2}$ is a rationalising factor of $\sqrt[3]{500}$.
ALITER $\sqrt[3]{500}=\sqrt[3]{125 \times 4}=\sqrt[3]{5^3 \times 4}=5\left(\sqrt[3]{2^2}\right)$
A rationalising factor of $\sqrt[3]{2^2}$ is $\sqrt[3]{2}$. Hence, the simplest rationalising factor of $\sqrt[3]{500}$ is $\sqrt[3]{2}$.
We find that
$\sqrt[3]{500} \times \sqrt[3]{2}=\sqrt[3]{500 \times 2}=\sqrt[3]{10^3}=10$, which is a rational number.
Hence, $\sqrt[3]{2}$ is a rationalising factor of $\sqrt[3]{500}$.
ALITER $\sqrt[3]{500}=\sqrt[3]{125 \times 4}=\sqrt[3]{5^3 \times 4}=5\left(\sqrt[3]{2^2}\right)$
A rationalising factor of $\sqrt[3]{2^2}$ is $\sqrt[3]{2}$. Hence, the simplest rationalising factor of $\sqrt[3]{500}$ is $\sqrt[3]{2}$.
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