Question

Which monomial is a perfect cube? 16x6 27x8 32x12 64x6

Answer 1

The fastest way is to just use a scientific calculator.

To do it without a calculator, use prime factorization.

I'll only do the second one which is the answer.

27 x 8

= 3^3 x 2^3 = 6^3

Which is a perfect cube.

Answer 2

ANSWER


$27 \times 8$

EXPLANATION


A perfect cube is a number that can be written in the form

${x}^{3}$


Let us use prime factorization to check which of the options is a perfect cube.



$16 \times 6 = {2}^{4} \times 2 \times 3 = {2}^{5} \times 3$


This is not a perfect cube.





$27 \times 8 = {3}^{3} \times {2}^{3} = {(2 \times 3)}^{3} = {6}^{3}$


This is a perfect cube.




$32 \times 12 = {2}^{5} \times {2}^{2} \times 3 = {2}^{7} \times 3$


Not a perfect cube.



$64 \times 6 = {2}^{6} \times 2 \times 3 = {2}^{7} \times 3$

This is also not a perfect cube.



The correct answer is B.