13.2k views
0 votes
Is 675 a perfect cube? if not then by which number it should be multiplied to obtain a perfect cube

User Skone
by
8.8k points

1 Answer

7 votes
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.
User Andiba
by
7.9k points

No related questions found