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    Hi everyone! I'm really stuck on a surds question - would anyone be able to help?

    This is the question...

    Work out the value of (√12 - √3)²

    How would you work it out, step by step?

    Thank you!
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    Any method with expanding brackets would work as (\sqrt12-\sqrt3)^2=(\sqrt12-\sqrt3)(\sqrt12-\sqrt3)

    Personally I would draw myself a mutiplication table with \sqrt12 and -\sqrt3.

    Remember the surd rule: \sqrt{a} \cdot \sqrt{b} = \sqrt{ab} and you can use this rule to split \sqrt12 into \sqrt{4\cdot 3}=\sqrt4 \cdot \sqrt3 = 2\sqrt3

    Table would look like this:

    \begin{array}{r|lc} \cdot & \sqrt12 & -\sqrt3 \\ \hline \sqrt12 & \sqrt12\sqrt12 & (\sqrt{12})(-\sqrt3) \\ -\sqrt3 & (\sqrt{12})(-\sqrt3) & (-\sqrt{3})(-\sqrt 3)}  \end{array}


    And just simplify these values then add them up.
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    (Original post by dowajuseyo)
    Hi everyone! I'm really stuck on a surds question - would anyone be able to help?

    This is the question...

    Work out the value of (√12 - √3)²

    How would you work it out, step by step?

    Thank you!
    (Original post by RDKGames)
    Any method with expanding brackets would work as (\sqrt12-\sqrt3)^2=(\sqrt12-\sqrt3)(\sqrt12-\sqrt3)

    Personally I would draw myself a mutiplication table with \sqrt12 and -\sqrt3.

    Remember the surd rule: \sqrt{a} \cdot \sqrt{b} = \sqrt{ab} and you can use this rule to split \sqrt12 into \sqrt{4\cdot 3}=\sqrt4 \cdot \sqrt3 = 2\sqrt3

    Table would look like this:

    \begin{array}{r|lc} \cdot & \sqrt12 & -\sqrt3 \\ \hline \sqrt12 & \sqrt12\sqrt12 & (\sqrt{12})(-\sqrt3) \\ -\sqrt3 & (\sqrt{12})(-\sqrt3) & (-\sqrt{3})(-\sqrt 3)}  \end{array}


    And just simplify these values then add them up.
    Much faster to simplify sqrt(12) first to 2sqrt(3). Then you just have 2sqrt(3)-sqrt(3) inside the bracket, which becomes sqrt(3), and then squaring gives the answer of 3 immediately.
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    (Original post by HapaxOromenon3)
    Much faster to simplify sqrt(12) first to 2sqrt(3). Then you just have 2sqrt(3)-sqrt(3) inside the bracket, which becomes sqrt(3), and then squaring gives the answer of 3 immediately.
    brb, gonna slap myself for not noticing that. I knew root 12 goes into 2root3 but didn't notice I can take one away from the other lol.

    :slap:
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    (Original post by dowajuseyo)
    Hi everyone! I'm really stuck on a surds question - would anyone be able to help?

    This is the question...

    Work out the value of (√12 - √3)²

    How would you work it out, step by step?

    Thank you!
    Step by step solutions aren't encouraged to be given here. I can relate all too well with being completely stuck with questions and not knowing where to begin, but it's often a good idea to remind yourself of the topic that you're given - eg in this case it is both surds and expanding the brackets (the square). Ask yourself what you know about each of those topics and how they could possibly be applied to the question, and try something - if you're still stuck after that you should post with your working.
 
 
 
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