Question

Find the cube-roots of:

(i) 2.744 (ii) 9.261 (iii) 0.000027

(iv) -0.512 (v)-15.625 (vi)-125 \times 1000

Answer 1

$\left(i\right)2.744=\sqrt[3]{3\frac{2744}{1000}}$

$=\sqrt[3]{3\frac{2\times 2\times 2\times 7\times 7\times 7}{10\times 10\times 10}}=\frac{2\times 7}{10}=\frac{14}{10}=1.4$

$\left(ii\right)9.261=\sqrt[3]{3\frac{9261}{1000}}=\sqrt{\frac{3\times 3\times 3\times 7\times 7\times 7}{10\times 10\times 10}}$

$=\frac{3\times 7}{10}=\frac{21}{10}=2.1$

$\left(iii\right)0.000027=\sqrt[3]{3\frac{27}{1000000}}=\sqrt[3]{3\frac{3\times 3\times 3}{100\times 100\times 100}}=\frac{3}{100}=0.03$

$\left(iv\right)-0.512=\sqrt[3]{3\frac{-512}{1000}}=\sqrt{\frac{-8\times -8\times -8}{10\times 10\times 10}}=\frac{-8}{10}=0.8$

$\left(v\right)-15.625=\sqrt[3]{3\frac{-15625}{1000}}$

$=\sqrt{\frac{-(5\times 5\times 5)\times (5\times 5\times 5)}{10\times 10\times 10}}=\frac{-5\times 5}{10}=\frac{-25}{10}=-2.5$

$\left(vi\right)-125\times 1000=\sqrt{-125\times 100}=\sqrt{-(5\times 5\times 5)\times (10\times 10\times 10)}=-5\times 10=-50$