Question

Find the cube root of $250047$ using prime factorization:

• A. $63$
• B. $61$
• C. $67$
• D. $65$

Answer 1

Answer: (A)

$63$

On prime factorising, we get,

$250047$ $=\underset{–}{3\times 3\times 3}\times \underset{–}{3\times 3\times 3}\times \underset{–}{7\times 7\times 7}$

$=3^3\times 3^3\times 7^3={63}^3$.

Then, cube root of $250047$ is:

$\sqrt[3]{3250047}=\sqrt[3]{3{63}^3}=63$.

Therefore, option $A$ is correct.