36x = 6*6*x...

So x should be equal to 6 to make it a cube...

.so x=6

Understanding the Problem:
We are given that 36x is a perfect cube number, and we need to find the possible values of x. In order to solve this problem, we need to understand the concept of perfect cubes and how to determine if a number is a perfect cube.

Perfect Cubes:
A perfect cube is a number that can be expressed as the cube of an integer. For example, 1, 8, 27, 64, etc., are perfect cubes because they can be expressed as 1^3, 2^3, 3^3, 4^3, etc., respectively.

Method to Solve:
To find the possible values of x, we need to determine the factors of 36x and check if they can be expressed as the cube of an integer. We can follow these steps to solve the problem:

Step 1: Factorize 36x
To factorize 36x, we need to find the prime factors of 36 and the value of x. The prime factors of 36 are 2, 2, 3, and 3, which can be written as 2^2 * 3^2.

Step 2: Express the factors as perfect cubes
We need to express the factors of 36x as perfect cubes. Since 2^2 * 3^2 = 36, we can express it as (2 * 3)^2 = 6^2. Therefore, 36 is a perfect cube.

Step 3: Determine the values of x
Now, we need to determine the possible values of x. Since 36 is a perfect cube, the value of x should also be a perfect cube.

Step 4: Find the perfect cube values of x
We can find the perfect cube values of x by taking the cube root of 36. The cube root of 36 is 6. Therefore, x can be equal to 6.

Conclusion:
In conclusion, the value of x is 6.