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Thread: Square root and simplest form

  1. #1
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    Square root and simplest form

    $\displaystyle \sqrt{\frac{18ab}{16b^4}} = \sqrt{\frac{9a}{8b^3}}$

    Is that in simplest form? There is probably something else I can do but I can't spot anything
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    Re: Square root and simplest form

    Quote Originally Posted by uperkurk View Post
    $\displaystyle \sqrt{\frac{18ab}{16b^4}} = \sqrt{\frac{9a}{8b^3}}$

    Is that in simplest form? There is probably something else I can do but I can't spot anything
    It really depends upon you mean by simplest form.

    You can say $\displaystyle \sqrt{\frac{18ab}{16b^4}} = \sqrt{\frac{9a}{8b^3}}=\frac{3}{2}\sqrt{\frac{a}{2 b}}$ .
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    Re: Square root and simplest form

    Quote Originally Posted by Plato View Post
    It really depends upon you mean by simplest form.

    You can say $\displaystyle \sqrt{\frac{18ab}{16b^4}} = \sqrt{\frac{9a}{8b^3}}=\frac{3}{2}\sqrt{\frac{a}{2 b}}$ .
    But would that be classed as "simpler" or just equally similar?

    Write in simplest radical form: $\displaystyle \sqrt[3]{54y^8}$ and I have no idea how to go about this.

    **EDIT** $\displaystyle \sqrt{(6y\times9y)^4}$ is this a start?
    Last edited by uperkurk; Aug 7th 2013 at 11:55 AM.
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    Re: Square root and simplest form

    Quote Originally Posted by uperkurk View Post
    But would that be classed as "simpler" or just equally similar?
    Well, I did say it depends on who is asking.

    Quote Originally Posted by uperkurk View Post
    Write in simplest radical form: $\displaystyle \sqrt[3]{54y^8}$ and I have no idea how to go about this.
    $\displaystyle \sqrt[3]{54y^8}=\sqrt[3]{(7)(2^3)(y^6)(y^2)}}=2y^2\sqrt[3]{7y^2}$
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    Re: Square root and simplest form

    Quote Originally Posted by Plato View Post
    Well, I did say it depends on who is asking.

    $\displaystyle \sqrt[3]{54y^8}=\sqrt[3]{(7)(2^3)(y^6)(y^2)}}=2y^2\sqrt[3]{7y^2}$
    I was actually asking you, in your opinion, which would you prefer to see?

    also did you mean $\displaystyle \sqrt[3]{(6)(3^3)(y^6)(y^2)}$ ?

    Also I can see how you worked it out, thanks.
    Last edited by uperkurk; Aug 7th 2013 at 12:02 PM.
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    Re: Square root and simplest form

    Quote Originally Posted by Plato View Post
    Well, I did say it depends on who is asking.



    $\displaystyle \sqrt[3]{54y^8}=\sqrt[3]{(7)(2^3)(y^6)(y^2)}}=2y^2\sqrt[3]{7y^2}$
    hello,

    I don't want to pick at and you but...

    $\displaystyle 7 \cdot 8 \ne 54$
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    Re: Square root and simplest form

    Quote Originally Posted by uperkurk View Post
    I was actually asking you, in your opinion, which would you prefer to see?

    also did you mean $\displaystyle \sqrt[3]{(6)(3^3)(y^6)(y^2)}$ ?

    Also I can see how you worked it out, thanks.
    ... probably you mean: $\displaystyle \sqrt[3]{(2)(3^3)(y^6)(y^2)}$
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    Re: Square root and simplest form

    Quote Originally Posted by earboth View Post
    ... probably you mean: $\displaystyle \sqrt[3]{(2)(3^3)(y^6)(y^2)}$
    wha?!!! now I'm mega confused... $\displaystyle (2)(9)=18$

    $\displaystyle (6)(9)=54$ ?
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    Re: Square root and simplest form

    Quote Originally Posted by earboth View Post
    hello,

    I don't want to pick at and you but...

    $\displaystyle 7 \cdot 8 \ne 54$
    I don't know what I was thinking. Of course it is 56.

    But $\displaystyle 54=2(3^3)$ so $\displaystyle \sqrt[3]{54}=3\sqrt[3]2$
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