find the smallest number by which 2560 must be multiplied so that the product a perfect cube.
Give the answer with pic plz.​

2 thoughts on “find the smallest number by which 2560 must be multiplied so that the product a perfect cube. <br />Give the answer with pic plz.​”

1. Interesting! If you factorize 2560 we get

   2560= 8^3 *5.

   If we multiply the number by 5^2=25, the result will be 8^3* 5^3, which is the perfect cube.

   So 25 is the smallest positive integer.

   But just wait, the multiplying factor can be fraction as well!

   If we multiply 2560 by (1/2560), the result is 1.

   1 itself is a perfect cube. So answer can be 1/2560.

   But wait again! Why it can’t be negative number? It can be.

   If we multiply 2560 by (-2560 * 2560), the result will be – 2560*2560*2560 which is a perfect cube. So answer can be -2560*2560.

   But wait, the story is not over yet. Any number of the form (- 2560*2560 * n^3), where n is a natural number, can be the answer. If 2560 is multiplied by this number the result is perfect cube & cube root will be -2560* n.

   So there is no definite one answer.

   Hope you followed what I have written.

   Reply

2. Answer:

   25

   Step-by-step explanation:

   Prime factorising 2560, we get,

   2560=2

   9

   ×5.

   We know, a perfect cube has multiples of 3 as powers of prime factors.

   Here, number of 2’s is 9 and number of 5’s is 1.

   So we need to multiply another 5

   2

   in the factorization to make 2560 a perfect cube.

   Hence, the smallest number by which 2560 must be multiplied to obtain a perfect cube is 5

   2

   =25.

   Reply