Question

Find the cube root of $-17576$ using factorization.

Answer 1

Let us first find the cube root of $17576$. As earlier, we have
$17576=2\times \left(8788\right)=2\times 2\times \left(4394\right)=2\times 2\times 2\times \left(2197\right)$
$=2\times 2\times 2\times 13\times \left(169\right)$
$=2\times 2\times 2\times 13\times 13\times 13$
$=(2\times 13)\times (2\times 13)\times (2\times 13)$
$=26\times 26\times 26$.
This shows that $-17576=(-26)\times (-26)\times (-26)$. Thus $\sqrt[3]{3-17576}=-26$.