What smallest number should 2560 be multiplied with so that the product becomes a perfect cube?

Text Solution

Solution : By using prime factorization we could find:<br>(i)`675`<br>`675=3^3times5^2`<br>As we can see that `5` is not cubed.<br>Hence, `5` is the smallest number by which `675` should be multiplied to make it a perfect cube.<br><br>(ii)`1323`<br>`1323=3^3times7^2`<br>As we can see that `7` is not cubed.<br>Hence, `7` is the smallest number by which `1323` should be multiplied to make it a perfect cube.<br>(iii)`2580`<br>`2560=2^9times5`<br>As we can see that `5` is not cubed.<br>Hence, `5times5=25` is the smallest number by which `2560` should be multiplied to make it a perfect cube.

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

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