Question

Find the cube root of 175616 by prime factorisation method. [3 marks]

Answer 1

Factoising 175616 using the prime factorisation method,

$\begin{array}{cc}2& 175616\\ 2& 87808\\ 2& 43904\\ 2& 21952\\ 2& 10976\\ 2& 5488\\ 2& 2744\\ 2& 1372\\ 2& 686\\ 7& 343\\ 7& 49\\ 7& 7\\ & 1\end{array}$

[2 marks]

$\sqrt[3]{3175616}=\sqrt[3]{32\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 7\times 7\times 7}=2\times 2\times 2\times 7=56\text{[1 mark]}$