Question

Find whether it is a perfect cube or not?
3375

Answer 1

Hint: To solve this type of problem first we have to factorize the given number and write the factors and check whether the perfect cube is there or not. The cube of a positive integer is another positive integer.

Complete step-by-step answer:
A perfect cube is any number that can be expressed as the product of three equal integers. In other words, a perfect cube is a number that can be made by cubing an integer. Every perfect cube is itself an integer.
Also, the perfect cube will have the same sign as the number you started with.
The cube of a negative integer is another negative integer.
The cube of zero is zero.

The given number is 3375
Now writing the prime factors for 3375
\[3375=5\times 675\]
\[3375=5\times 5\times 135\]
\[3375=5\times 5\times 5\times 27\]
\[3375=5\times 5\times 5\times 3\times 9\]
\[3375=5\times 5\times 5\times 3\times 3\times 3\]
We can further write the above prime factors as
\[3375=15\times 15\times 15\]
\[3375={{15}^{3}}\] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (a)
From (a) we can say that there exists a perfect cube root for 3375.

Note: From (a) we can say it is a perfect cube. For a number to become a perfect cube it should have the same number multiplied thrice. This is a direct problem, just by factoring we can say whether it is a perfect cube or not.