Question

Find the cube root of the number 2460375 using the fact that $2460375=3375\times 729.$

• A. 125
• B. 135
• C. 145
• D. 155

Answer 1

The correct option is B 135

$\text{Given number:}2460375=3375\times 729\sqrt[3]{32460375}=\sqrt[3]{33375}\times \sqrt[3]{3729}$
Prime factorisation of 3375:
$\begin{array}{cc}3& 3375\\ 3& 1125\\ 3& 375\\ 5& 125\\ 5& 25\\ 5& 5\\ & 1\end{array}$
$\sqrt[3]{33375}=\sqrt[3]{33\times 3\times 3\times 5\times 5\times 5}$
$\begin{array}{cc}3& 729\\ 3& 243\\ 3& 81\\ 3& 27\\ 3& 9\\ 3& 3\\ & 1\end{array}$
$\sqrt[3]{3729}=\sqrt[3]{33\times 3\times 3\times 3\times 3\times 3}$
Thus, $\sqrt[3]{32460375}=\sqrt[3]{33\times 3\times 3\times 5\times 5\times 5}\times \sqrt[3]{33\times 3\times 3\times 3\times 3\times 3}\sqrt[3]{32460375}=15\times 9\sqrt[3]{32460375}=135$