Question

The cube root of 9000 is _____.
(solve by prime factorisation method)

• A. $20\sqrt[3]{39}$
• B. $10\sqrt[3]{39}$
• C. $20\sqrt[3]{36}$
• D. $10\sqrt[3]{36}$

Answer 1

The correct option is B $10\sqrt[3]{39}$

$\begin{array}{cc}2& 9000\\ 2& 4500\\ 2& 2250\\ 3& 1125\\ 3& 375\\ 5& 125\\ 5& 25\\ 5& 5\\ & 1\end{array}$
$\Rightarrow$9000 = 2 $\times$ 2 $\times$ 2 $\times$ 3 $\times$ 3 $\times$ 5 $\times$5 $\times$ 5
$\sqrt[3]{39000}$ = $\sqrt[3]{3(2^3\times 3^2\times 5^3)}$ = $10\sqrt[3]{39}$