Question

Which of the following statements are true?

Select all that apply.
A. 16 is a perfect cube.
B. 42 is neither a perfect square nor a perfect cube.
C. 2,197 is both a perfect square and a perfect cube.
D. 64 is a perfect cube.
E. 121 is a perfect square.

Answer 1

Explanation:

A

16 = 4×4 or 2×2×2×2

no triple factors.

so, this is wrong.

B.

42 = 7×6 = 7÷3÷2

no triple factors.

so, this is wrong.

C.

2197 = 13³ = 13×13×13 (a perfect cube).

that's it, there are no other factors possible, because 13 is a prime number.

so, they're cannot be suddenly 2 identical numbers that create 2197 out of their product.

so, this is wrong

D.

64 = 8×8 = 4×4×4 ÷ 2×2×2×2×2×2

this is true.

E.

121 = 11×11

abs that's it. again we are having prime numbers as factors. no more sub-factoring is possible.

but it did not matter. this reveals itself as perfect square.

this is true.