Question
Evaluate: $125\sqrt[3]{\text{a}^6}-\sqrt[3]{125\text{a}^6}$
✓
Answer
Property:
For any two integers a and b, $\sqrt[3]{\text{ab}}=\sqrt[3]{\text{a}}\times\sqrt[3]{\text{b}},$
From the above property, we have:
$125\sqrt[3]{\text{a}^6}-\sqrt[3]{125\text{a}^6}$
$=125\sqrt[3]{\text{a}^6}\Big(\sqrt[3]{125}\times\sqrt[3]{\text{a}^6}\Big)$
$= 125 \times a^2- (5 \times a^2)$
$\Big(\because\sqrt[3]{\text{a}\times\text{a}\times\text{a}\}\times\text{\{a}\times\text{a}\times\text{a}\}}= \text{a} \times \text{a} = \text{a}^2 \text{and}\sqrt[3]{125}= \sqrt[]{5\times5\times5}=5\Big)$
$= 125a^2- 5a^2$
$= 120a^2$
For any two integers a and b, $\sqrt[3]{\text{ab}}=\sqrt[3]{\text{a}}\times\sqrt[3]{\text{b}},$
From the above property, we have:
$125\sqrt[3]{\text{a}^6}-\sqrt[3]{125\text{a}^6}$
$=125\sqrt[3]{\text{a}^6}\Big(\sqrt[3]{125}\times\sqrt[3]{\text{a}^6}\Big)$
$= 125 \times a^2- (5 \times a^2)$
$\Big(\because\sqrt[3]{\text{a}\times\text{a}\times\text{a}\}\times\text{\{a}\times\text{a}\times\text{a}\}}= \text{a} \times \text{a} = \text{a}^2 \text{and}\sqrt[3]{125}= \sqrt[]{5\times5\times5}=5\Big)$
$= 125a^2- 5a^2$
$= 120a^2$
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