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Ratling [72]
4 years ago
15

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

Mathematics
2 answers:
miss Akunina [59]4 years ago
5 0
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.
navik [9.2K]4 years ago
4 0
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.
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