Perfect Cube 735

What is the smallest positive integer by which you can multiply 735 so that the product is a perfect cube?
Source: mathcontest.olemiss.edu 4/14/2008

SOLUTION
Example of a perfect cube: 216=27\cdot 8=3^3\cdot 2^3.

735=3\cdot 5\cdot 7^2.
To make 735 a perfect cube all we have to do is multiply it by 3^2\cdot 5^2\cdot 7=1575 so that we end up with 3\cdot 3^2\cdot 5\cdot 5^2\cdot 7^2\cdot 7=3^3\cdot 5^3\cdot 7^3 a perfect cube.

Check
735\cdot 1575=1157625
\sqrt[3]{1157625}=105

Answer: 1575.

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About mvtrinh

Retired high school math teacher.
This entry was posted in Problem solving and tagged , . Bookmark the permalink.

2 Responses to Perfect Cube 735

  1. vinod kumar says:

    sir, please provide me solution of
    Question:-find the least number which is added to 200 to make it a perfect cube.

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