Question

by which smallest number should 5324 be multiplied so that the product is a perfect cube

Answer 1

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Answer 2

Answer:

We have to multiply the given number by 2 to make a perfect cube.

Step-by-step explanation:

The given number is 5324. Let us find the prime factorization of this number.

5324 =2 × 2 × 11 × 11 × 11

We can rewrite this as

5324 =2^2 × 11^3

Now, in perfect cube, we need the numbers which occurs the trice. we can take the numbers out of the cubic root.

In the above factorization, 11 occurs thrice and 2 occurs twice. Hence, in order to make the perfect cube we need an extra 2 so that it becomes 2^3.

Hence, we have to multiply the given number by 2 to make a perfect cube.