SOLUTION: you multiply a number by the square root of that number. The cube of the result is 317 less than 20,000. what is the number?

Algebra ->  Square-cubic-other-roots -> SOLUTION: you multiply a number by the square root of that number. The cube of the result is 317 less than 20,000. what is the number?      Log On


   



Question 1089464: you multiply a number by the square root of that number. The cube of the result is 317 less than 20,000. what is the number?
Answer by ikleyn(52834) About Me  (Show Source):
You can put this solution on YOUR website!
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Let "x" be the number under the question.


Then the condition says


%28x%2Asqrt%28x%29%29%5E3 = 20000 - 317,   or, which is the same,   x^(9/2) = 19683,   or


%28sqrt%28x%29%29%5E9 = 3%5E9.


It implies sqrt%28x%29 = 3.


Hence,  x = 3%5E2 = 9.


Answer.  x = 9.


Check.  x%2Asqrt%28x%29 = 9%2A3 = 27  and  27%5E3 = 19683.  ! Correct !.

Solved.