Question

Find the cube root of the following numbers by prime fractorisaiton method.

$343$

$4096$

$5832$

$125000$

Answer 1

Finding the cube root of each of the given number by representing them as a product of their prime factors:

$i)343=7\times 7\times 7$

$=7^3$

Hence, $\sqrt[3]{3343}=7$

$ii)4096=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2$

$=2^{12}$

$=2^{4^3}$

Hence, $\sqrt[3]{34096}=2^4=16$

$iii)5832=3\times 3\times 2\times 3\times 3\times 2\times 3\times 3\times 2$

$=(3^2\times 2{)}^3$

Hence, $\sqrt[3]{35832}=3^2\times 2=18$

$iv)125000=2\times 2\times 2\times 5\times 5\times 5\times 5\times 5\times 5$

$=2^3\times 5^3\times 5^3$

$=(2\times 5{)}^3\times 5^3$

$=(5\times 10{)}^3$

Hence, $\sqrt[3]{3125000}=5\times 10=50$