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

Find the smallest number by which 2560 must be multiplied so that the

1.	Find the smallest number by which 2560 must be multiplied so that the product is a perfect cube.
Answer» - The smallest number by which 2560 must be multiplied so that the PRODUCT is a perfect cube is 25. SOLUTION The given number = 2560.Here , we have to find the smallest number by which 2560 must be multiplied so that the product is a perfect cube.To find the smallest number by which 2560 must be multiplied so that the product is a perfect cube , first we must do the prime factorization of 2560.2560 = 2×2×2×2×2×2×2×2×2×5On PAIRING,2560 = 2×2×2×2×2×2×2×2×2×5Here only 5 is left unpaired.∵ In finding perfect cube pairing is done with 3 numbers.For 5 to become a pair of 5 it must be multiplied by 5².∴ The Smallest number by which 2560 must be multiplied so that the product is a perfect cube = 5² = 5 × 5 = 25.LET US VERIFY 2560 × 25 = 64000∵ The answer we obtained is a perfect cube our answer is correct.