Question

Question 97

Solve the following question:

Using prime factoristaion, find the cube roots of

a) 512
b) 2197

Answer 1

a) We have, 512
$\begin{array}{cc}2& 512\\ 2& 256\\ 2& 128\\ 2& 64\\ 2& 32\\ 2& 16\\ 2& 8\\ 2& 4\\ 2& 2\\ & 1\end{array}$
Now, $512=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times$
$\therefore \sqrt[3]{3512}=2\times 2\times 2$
= 8

b) We have, 2197
$\begin{array}{cc}13& 2197\\ 13& 169\\ 13& 13\\ & 1\end{array}$
Now, $2197=13\times 13\times 13$
$\therefore \sqrt[3]{32197}=13$