Question

The cube root of $-\frac{125}{1331}$ is:

• A. $\frac{5}{11}$
• B. $-\frac{5}{11}$
• C. $\frac{13}{25}$
• D. None of these

Answer 1

The correct option is B $-\frac{5}{11}$

On prime factorisation of the numbers individually, we get,

$125=\underset{–}{5\times 5\times 5}=5^3$.

$1331=\underset{–}{11\times 11\times 11}={11}^3$.

Then, cube root of $-\frac{125}{1331}$ is:

$\sqrt[3]{3-\frac{125}{1331}}$ $=\sqrt[3]{3-\frac{5^3}{{11}^3}}$ $=\sqrt[3]{3(-\frac{5}{11}{)}^3}$ $=-\frac{5}{11}$.

Thus, option $B$ is correct.