Question

1.Find the smallest number by which 1323 must be multiplied so that the product is a perfect cube.

2.What is the smallest number by which 1600 must be divided so that the quotient is a perfect cube?

3.Find the smallest number by which 2560 must be multiplied so that the product is a perfect cube.​

Answer 1

Answer:

1.In order for 1323 to become a perfect cube, we need to multiply it by 7. This will give us 9261 and the cube root will be 21

2.To solve this question, we will start with factorising the given number 1600,

where we will get some factors of the number, then we will make group of three (because as it is given that it needs to be perfect cube), so, after arranging the factors into group of three, the remaining number will be our required answer.

Step-by-step explanation:

2.We have been given a number, i.e., 1600,

we need to find the smallest number by which 1600

must be divided so that the quotient is a perfect cube.

The given number is 1600,

so we will start with factorizing the number 1600.

On factorization the number, we get

1600 = 2×2×2×2×2×2×5×5

So, we get the factors of 1600,

now we need to group the numbers in a group of three since it is given in the question that it has to be a perfect cube.

We can see above that the number 5

does not form a triplet, because it only contains two 5′s.

Hence, the number, 5×5=25,

i.e., 25

has to be divided so that the quotient becomes a perfect cube.

Thus, the smallest number by which 1600

must be divided so that the quotient is a perfect cube is 25.