Answer:
No, 675 is not a perfect cube because it cannot be expressed as the cube of a whole number.
675 x 3 x 5 = 10125 which is a perfect cube
Explanation:
To find the number by which 675 should be multiplied to obtain a perfect cube, we can factorize 675 into its prime factors:
675 = 3 x 3 x 3 x 5 x 5
To make this number a perfect cube, we need to multiply it by another number that will bring the exponent of each prime factor to a multiple of 3. So we can multiply 675 by one more factor of 3 and one more factor of 5, like this:
675 x 3 x 5 = 10125
Now, 10125 can be expressed as the cube of 15, which means that 675 x 3 x 5 is a perfect cube. Therefore, 675 should be multiplied by 3 x 5, or 15, to obtain a perfect cube.