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Thread: How do I simplify this expression?

  1. #1
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    Post How do I simplify this expression?




    250X^9y^5 all inside a 3rd root thing...
    The answer is 5X^3 Y^3 and then a "2y^2" which is inside a square root thing.
    Thanks a lot!
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  2. #2
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    Quote Originally Posted by hersheybar11 View Post



    250X^9y^5 all inside a 3rd root thing...
    The answer is 5X^3 Y^3 and then a "2y^2" which is inside a square root thing.
    Thanks a lot!
    $\displaystyle \sqrt[3]{250 x^9 y^5}$

    Since that is a cube root, set everything into cubes as much as possible.

    250= 125* 2 and 125= 5*5*5= $\displaystyle 5^3$

    $\displaystyle x^9= (x*x*x)(x*x*x)(x*x*x)= (x^3)^3$

    $\displaystyle y^5= y*y*y*y*y= (y*y)(y*y*y)= y^2 y^3$

    So what that is is $\displaystyle \sqrt[3]{2(5^3)(x^3)^3y^2y^3}$
    Of course, the definition of "cube root" is that $\displaystyle \sqrt[3]{a^3}= a$.

    $\displaystyle \sqrt[3]{250 x^9 y^5}= \sqrt[3]{2}\sqrt[3]{5^3}\sqrt[3]{(x^3)^3}\sqrt[3]{y^2}\sqrt[3]{y^3}$

    $\displaystyle = \sqrt[3]{2}(5)(x^3)\sqrt[3]{y^2}y= 5x^3y\sqrt[3]{2y^2}$
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