Question:
Evaluate:
$\sqrt[3]{-512}$
Solution:
$\sqrt[3]{-512}$
By prime factorisation:.png)
$\sqrt[3]{512}=2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2$
$\quad=(2 \times 2 \times 2) \times(2 \times 2 \times 2) \times(2 \times 2 \times 2)$
$\sqrt[3]{-512}=-\sqrt[3]{(2 \times 2 \times 2)}=-8$
$\therefore \sqrt[3]{-512}=-(\sqrt[3]{512})=-8$
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