Question

Find the cube-roots of :

(i) $700\times 2\times 49\times 5$ (ii) $-216\times 1728$ (iii) $-64\times -125$

(iv) $-\frac{27}{343}$ (v) $\frac{729}{-1331}$ (vi) 250.047 (vii) -175616

Answer 1

$\left(i\right)700\times 2\times 49\times 5$

$=2\times 2\times 5\times 5\times 7\times 2\times 7\times 7\times 5=(2\times 2\times 2)\times (5\times 58\times 5)\times (7\times 7\times 7)=2\times 5\times 10=70$

$\left(ii\right)-216\times 1728$

$=(2\times 2\times 2\times 3\times 3\times 3)\times (2\times 2\times 2\times 2\times 2\times 2\times 3\times 3\times 3)=-2\times 3\times 2\times 2\times 3=-72$

$\left(iii\right)-64\times -125=-(4\times 4\times 4)\times -(5\times 5\times 5)=-4\times -5=20\left(iv\right)-\frac{27}{343}=\frac{3\times 3\times 3}{7\times 7\times 7}=-\frac{3}{7}\left(v\right)\frac{729}{-1331}=\frac{-(9\times 9\times 9)}{-(11\times 11\times 11)}=-\frac{9}{11}\left(vi\right)250.047=\frac{250047}{1000}$

$=\frac{(3\times 3\times 3)\times (3\times 3\times 3)\times (7\times 7\times 7)}{(10\times 10\times 10)}=\frac{3\times 3\times 7}{10}=\frac{63}{10}=6.3$

(vii) -175616

$=-\left[\right(2\times 2\times 2)\times (2\times 2\times 2)\times (2\times 2\times 2)\times (7\times 7\times 7\left)\right]=-[2\times 2\times 2\times 7]=-56$