Which of the following numbers are not perfect cubes?

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216

125

1000

46656

answer is D.

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Detailed Solution

Concept- By factoring each number in the choice, we can discover the cube root and determine which number does not have a perfect cube, which will help us solve the problem. You will get the right answers if you do this.
We shall first determine whether or not 216 is a perfect cube. To obtain the numbers, we shall factorise the word.
Since we are aware that 216 may be expressed as

, it is obvious that 6 is the cube root of 216, or

.
Next, we'll look at 125's cube root. We will factor the term to obtain the numbers regardless of whether it is a perfect cube or not.
We can see that 4 is the cube root of 64 because

and we know that 125 may be expressed as

.
Then, in order to determine whether the cube root of 1000 is a perfect cube or not, we shall factorise the expression.
We can see that 10 is the cube root of 1000, or

, as we know that 1000 may be expressed as

.
Next, we'll look at 100's cube root. We will factor the term to obtain the numbers regardless of whether it is a perfect cube or not.
We can see without a doubt that 46656 has no cube root because we are aware that it may be represented as

.
Hence, the correct answer is option 4.

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