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Math Help - square root + cube root of a number

  1. #1
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    square root + cube root of a number

    The square root and cube root of a number is equal to 36. What is the number ?

    Can this really be solved by logarithms ?

    I got far as log ( 36 - y raised to 1/2 ) = log y

    I don't know what to do next ?
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  2. #2
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    e^(i*pi)'s Avatar
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    \sqrt{x} + \sqrt[3]{x} = 36 \: \: , \: x \geq 0


    Logarithms seem like more trouble than they're worth.

    Let u = \sqrt[6]{x} \implies x = u^6 (6 is the LCD of 2 and 3).

    Thus we get f(u) = u^3 + u^2 - 36 = 0. u^3 comes from the rules of surds, namely: \sqrt{a} = a^{1/2} = a^{3/6} = \sqrt[6]{a^3} = u^3


    Solve the polynomial for u and then it should be trivial to find the value of x but remember to check for extraneous results and that any solution is in the domain


    edit 2: Hint f(3) = 0



    If you don't mean adding them then please clarify what the question wants
    Last edited by e^(i*pi); December 5th 2010 at 11:44 AM. Reason: went for a polynomial approach
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  3. #3
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    You're the man !
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