divide the number 52728 by the smallest number so that the question is a perfect cube. also find the cube root of the quotient.
Don't you mean "quotient", not "question"? How can a question have a square root?
52728 = 8*6591
= 2^3*3*2197
= 2^3*3*13^3
= 26^3*3
Divide by three and the cube root of the quotient is 26
To make the question a perfect cube, we need to divide the number 52728 by the smallest number that, when divided into it, results in a perfect cube.
To find the smallest number that makes the question a perfect cube, we can start by finding the prime factorization of 52728.
The prime factorization of 52728 is:
2^3 * 3^4 * 7^2
In order to make this number a perfect cube, we need all the exponents to be divisible by 3.
The smallest number to divide by would be 2^3 * 3^2 * 7^2, as this would divide out the highest power of 3 and leave a perfect cube.
The quotient when dividing 52728 by 2^3 * 3^2 * 7^2 is:
52728 / (2^3 * 3^2 * 7^2) = 468
Now, to find the cube root of the quotient, we take the cube root of 468.
The cube root of 468 is approximately 7.942.