Question 84

State whether the following statement is true or false:

$\sqrt[3]{8 + 27} = \sqrt[3]{8} + \sqrt[3]{27}$

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Solution

False
We have, $\sqrt[3]{8 + 27} \neq \sqrt[3]{8} + \sqrt[3]{27}$
[ $∵ \sqrt[3]{8} + \sqrt[3]{27} = \sqrt[3]{2 \times 2 \times 2} + \sqrt[3]{3 \times 3 \times 3} = 2 + 3 = 5$ ]
But, $\sqrt[3]{8 + 27} = \sqrt[3]{35} \neq \sqrt[3]{125} = 5$

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