Question

Find cube root of the following numbers by prime factorisation method.
(i) $64$
(ii) $512$
(iii) $10648$
(iv) $27000$
(v) $15625$
(vi) $13824$
(vii) $110592$
(viii) $46656$
(ix) $175616$
(x) $91125$

Answer 1

(i) $64=2\times 2\times 2\times 2\times 2\times 2=$ $2^3\times 2^3=4^3$
$\sqrt[3]{364}=4$
(ii) $512=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2$
$=$ $2^3\times 2^3\times 2^3=8^3$
$\sqrt[3]{3512}=8$
(iii) $10648=$ $2^3\times {11}^3={22}^3$
$\sqrt[3]{310648}=22$
(iv) $27000=$ $2^3\times 3^3\times 5^3$$={30}^3$
$\sqrt[3]{327000}=30$
(v) $15625=$ $5^3\times 5^3={25}^3$
$\sqrt[3]{315625}=25$
(vi) $13824=$ $2^3\times 2^3\times 2^3\times 3^3={24}^3$
$\sqrt[3]{313824}=24$
(vii) $110592=$ $2^3\times 2^3\times 2^3\times 2^3\times 3^3$$={48}^3$
$\sqrt[3]{3110592}=48$
(viii) $46656=$ $2^3\times 2^3\times 3^3\times 3^3$ $={36}^3$
$\sqrt[3]{346656}=36$
(ix) $175616=$ $2^3\times 2^3\times 2^3\times 7^3$$={56}^3$
$\sqrt[3]{3175616}=56$
(x) $91125=$ $5^3\times 3^3\times 3^3$ $={45}^3$
$\sqrt[3]{391125}=45$