Question

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

Answer 1

for this first we have to find its factors and make the pair of three.The factors are 2^9 ×5 . the 5 is alone and not making pair as it wants two multiples of 5 to make the pair of three so the smallest number is 5×5=25

Answer 2

Answer:

Smallest number to be multiplied is $5^{2}=25$    

Step-by-step explanation:

Factorization is the process of simplifying the number based on its factors or divisors.

Now, we need to find the smallest number by applying the factorization to the given number.

Now, by factorizing the given number, we get,  

$\therefore 2560=2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 5=2^{9} \times 5$

The nearest perfect cube is obtained by multiplying $2^{9} \text { and } 5^{3}$

Therefore, the nearest perfect cube of $2^{9} \times 5=2^{9} \times 5^{3}$

Hence, the smallest number to be multiplied is $5^{2}=25$