Single Choice

Find the cube root of $$438976$$ using prime factorization:

A$$74$$
B$$72$$
C$$76$$
Correct Answer
D$$71$$

Solution

$$\displaystyle 438976={ \left( 2 \right) }^{ 6 }\times { \left( 19 \right) }^{ 3 }$$
$$\displaystyle \sqrt [ 3 ]{ 438976 } ={ 2 }^{ 2 }\times 19$$
$$\displaystyle =2\times 2\times 19$$
$$\displaystyle =76$$

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