Question

Which of the following numbers are not perfect cubes?
A. 216
B. 125
C. 1000
D. 46656

Answer 1

Hint: In order to solve this problem we will find the cube root by factoring each number in the option then we will get to know which number does not have the perfect cube. Doing this will give you the right answers.

Complete step-by-step answer:
We will check 216 first that it is a perfect cube or not. We will factorize the term to get the numbers.
We know that 216can be written as 6 x 6 x 6 = 216 so we can clearly see that 6 is the cube root of 216 that is $\sqrt[3]{{216}} = 6$.
Then we will check the cube root of 125. Whether it is a perfect cube or not we will factorize the term to get the numbers.
We know that 125 can be written as 5 x 5 x 5 = 125 so we can clearly see that 4 is the cube root of 64 that is $\sqrt[3]{{125}} = 5$.
Then we will check the cube root of 1000 that is it a perfect cube or not we will factorize the term to get the numbers.
We know that 1000 can be written as 10 x 10 x 10 = 1000 so we can clearly see that 10 is the cube root of 1000 that is $\sqrt[3]{{1000}} = 10$.
Then we will check the cube root of 100. Whether it is a perfect cube or not we will factorize the term to get the numbers.
We know that 46656 can be written as 24 x 24 x 81 = 46656 so we can clearly see that there is no cube root of 46656.
So, the correct option is D.

Note: In this problem you need to know that the cube root of a number is a special value that, when used in a multiplication three times, gives that number. Example: 3 × 3 × 3 = 27, so the cube root of 27 is 3. Only some number is a perfect cube of a number. Knowing this will solve your problem.