QUESTION

# Which of the following are not perfect cubes?A. 216B. 128C. 1000D. 100E. 46656

Hint: To check if the number is a cube of a natural number, we compute the cube root of the given number, if the cube root obtained is a whole number, then we say that the given number is a cube of natural number.

Complete Step-by-Step solution:
To solve this question, we proceed according to the above explanation.
Now we are given options in the question. We will take them separately and check if we obtain a natural number by taking the cube root of them.
Now computing the cube root of the numbers in the option we have,
A. $\sqrt[3]{216}=6$, we obtained a natural number.
Therefore, 216 is a cube of a natural number.
B. $\sqrt[3]{128}=5.03$, we obtained a fraction and not a natural number.
Therefore, 128 is not a cube of a natural number.
C. $\sqrt[3]{1000}=10$, we obtained a natural number.
Therefore, 1000 is a cube of a natural number.
D. $\sqrt[3]{100}=4.64$, we obtained a fraction and not a natural number.
Therefore, 100 is not a cube of a natural number.
E. $\sqrt[3]{46656}=36$, we obtained a natural number.
Therefore, 46656 is a cube of a natural number.
Hence, we get our result as 128, and 100 aren’t a cube of a natural number.
Therefore, the correct options are (b) and (d).

Note: The possibility of error in this question can be using the fraction value also as a natural number which would be wrong because there does not exist any fraction or negative integer in N, the set of natural numbers. So always check before using any number as a natural number.