Question

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

Answer 1

Answer:-

$\red\bigstar$ 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 = 2×2×2×2×2×2×2×2×2×5

On pairing,

2560 = 2×2×2×2×2×2×2×2×2×5

Here 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

$\sqrt[3]{64000} = 40$

∵ The answer we obtained is a perfect cube our answer is correct.