Question

Find the cube root of the following number by prime factorisation method:

$512$

• A. $6$
• B. $8$
• C. $7$
• D. $9$

Answer 1

Answer: (B)

$8$

Prime factorising, we get,

$512=\underset{–}{2\times 2\times 2}\times \underset{–}{2\times 2\times 2}\times \underset{–}{2\times 2\times 2}$

$=\underset{–}{8\times 8\times 8}$.

Here, the factor $8$ occur as triplet. Hence, it is a perfect cube.

Therefore, cube root of $512$, i.e. $\sqrt[3]{3512}=8$.