MCQ
Mark $(\checkmark)$ against the correct answer: $\sqrt[3]{\frac{-343}{729}}=\ ?$
- A$\frac{7}{9}$
- ✓$\frac{-7}{9}$
- C$\frac{-9}{7}$
- D$\frac{9}{7}$
✓
Answer
Correct option: B.
$\frac{-7}{9}$
By prime factorisation method
$\sqrt[3]{\frac{-343}{729}}$
$=\frac{\sqrt[3]{-343}}{\sqrt[3]{729}}$
$=\frac{\sqrt[3]{(-7)\times(-7)\times(-7)}}{\sqrt[3]{3\times3\times3\times3\times3\times3}}$
$=\frac{\sqrt[3]{(-7)^3}}{\sqrt[3]{(3)^3\times(3)^3}}$
$=\frac{\sqrt[3]{(-7)^3}}{\sqrt[3]{(9)^3}}$
$=\frac{-7}{9}$
$\therefore\sqrt[3]{\frac{-343}{729}}=\frac{-7}{9}$
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