Question
Evaluate the following:
$\sqrt[3]{1000}+\sqrt[3]{0.008}-\sqrt[3]{0.125}$
$\sqrt[3]{1000}+\sqrt[3]{0.008}-\sqrt[3]{0.125}$
✓
Answer
To evaluate the value of the given expression, we need to proceed as follows:
$\sqrt[3]{1000}+\sqrt[3]{0.008}-\sqrt[3]{0.125}$
$=\sqrt[3]{10\times10\times10}+\sqrt[3]{\frac{8}{1000}}-\sqrt[3]{\frac{125}{1000}}$
$=\sqrt[3]{10\times10\times10}+{\frac{\sqrt[3]{8}}{\sqrt[3]{1000}}}-{\frac{\sqrt[3]{125}}{\sqrt[3]{1000}}}$
$=\sqrt[3]{3\times3\times3}+{\frac{\sqrt[3]{2^3}}{\sqrt[3]{1000}}}-{\frac{\sqrt[3]{5^3}}{\sqrt[3]{1000}}}$
$=10+\frac{2}{10}-\frac{5}{10}$
$=10+0.2-0.5$
$=9.7$
Thus, the answer is 9.7.
$\sqrt[3]{1000}+\sqrt[3]{0.008}-\sqrt[3]{0.125}$
$=\sqrt[3]{10\times10\times10}+\sqrt[3]{\frac{8}{1000}}-\sqrt[3]{\frac{125}{1000}}$
$=\sqrt[3]{10\times10\times10}+{\frac{\sqrt[3]{8}}{\sqrt[3]{1000}}}-{\frac{\sqrt[3]{125}}{\sqrt[3]{1000}}}$
$=\sqrt[3]{3\times3\times3}+{\frac{\sqrt[3]{2^3}}{\sqrt[3]{1000}}}-{\frac{\sqrt[3]{5^3}}{\sqrt[3]{1000}}}$
$=10+\frac{2}{10}-\frac{5}{10}$
$=10+0.2-0.5$
$=9.7$
Thus, the answer is 9.7.
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