Question

Find the cube root of 46656 by prime factorisation method. [3 marks]

Answer 1

Factorising 46656 by prime factorisation method,

$\begin{array}{cc}2& 46656\\ 2& 23328\\ 2& 11664\\ 2& 5832\\ 2& 2916\\ 2& 1458\\ 3& 729\\ 3& 243\\ 3& 81\\ 3& 27\\ 3& 9\\ 3& 3\\ & 1\end{array}$

[2 marks]

$\sqrt[3]{346656}=\sqrt[3]{32\times 2\times 2\times 2\times 2\times 2\times 3\times 3\times 3\times 3\times 3\times 3}=2\times 2\times 3\times 3=36\text{[1 mark]}$