Choose the correct answer.The number 45g is a perfect cube. Find the smallest positive integer value of g24854775
Question
Choose the correct answer.The number 45g is a perfect cube. Find the smallest positive integer value of g24854775
Solution 1
The question is asking for the smallest positive integer value of g such that 45g is a perfect cube.
A perfect cube is a number that can be expressed as the cube of an integer.
First, let's factorize 45. The prime factorization of 45 is 3^2 * 5.
For 45g to be a perfect cube, each prime factor must appear in multiples of 3 in the factorization.
We already have two 3's from 45, so we don't need any more 3's.
However, we only have one 5 from 45. To make 45g a perfect cube, we need two more 5's.
Therefore, the smallest positive integer value of g that makes 45g a perfect cube is 5^2, which is 25.
Solution 2
The question is asking for the smallest positive integer value of 'g' that would make 45g a perfect cube.
A perfect cube is a number that can be expressed as the cube of an integer. For example, 8 is a perfect cube because it can be expressed as 2^3.
First, let's factorize 45. The prime factorization of 45 is 3^2 * 5.
For 45g to be a perfect cube, each prime factor must appear a multiple of 3 times.
We already have two 3's from 45, so we don't need any more 3's. However, we only have one 5, and we need two more to make a multiple of 3.
Therefore, the smallest positive integer value of 'g' that would make 45g a perfect cube is 5^2, which is 25.
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