Maths year 11

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TMUA discussion - please read before posting 09-11-2016
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    Correct. What about something like \displaystyle \frac{1}{2+\sqrt{3}} ? It would be the same method with a slight twist.

    To firstly investigate, think about what happens when you multiply the denominator by 2+\sqrt{3} and then see what happens if you multiply it by 2-\sqrt{3}. This may prove to be quite challenging but I believe it would appear at the end of Higher papers.
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    (Original post by RDKGames)
    Correct. What about something like \displaystyle \frac{1}{2+\sqrt{3}} ? It would be the same method with a slight twist. To firstly investigate, think about what happens when you multiply the denominator by 2+\sqrt{3} and then see what happens if you multiply it by 2-\sqrt{3}. This may prove to be quite challenging.
    Yeah I get stuck on the expand and simplifying ones



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    (Original post by RDKGames)
    Correct. What about something like \displaystyle \frac{1}{2+\sqrt{3}} ? It would be the same method with a slight twist. To firstly investigate, think about what happens when you multiply the denominator by 2+\sqrt{3} and then see what happens if you multiply it by 2-\sqrt{3}. This may prove to be quite challenging.
    Yeah I get stuck on the expand and simplifying ones
    .


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    (Original post by z_o_e)
    Yeah I get stuck on the expand and simplifying ones
    .


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    You expanded correctly (though the last bracket should have a multiplication sign!). Now it's just a matter of collecting the terms. Remember the surd rule: \sqrt{a} \cdot \sqrt{b} = \sqrt{a\cdot b} and the fact that you cannot simplify something like 2\sqrt3 any further, so you leave that as it is.
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    (Original post by RDKGames)
    You expanded correctly (though the last bracket should have a multiplication sign!). Now it's just a matter of collecting the terms. Remember the surd rule: \sqrt{a} \cdot \sqrt{b} = \sqrt{a\cdot b} and the fact that you cannot simplify something like 2\sqrt3 any further, so you leave that as it is.


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    Actually, hold on. There is a mistake in your expansions I missed. The last bracket should be -\sqrt2 \cdot 2. Look at the arrows coming out for the first bracket, you have 3 from \sqrt3 and only 1 from \sqrt2 which means you are doing an extra needless calculation which you've already covered. Check it.
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    (Original post by RDKGames)
    Actually, hold on. There is a mistake in your expansions I missed. The last bracket should be -\sqrt2 \cdot 2. Look at the arrows coming out for the first bracket, you have 3 from \sqrt3 and only 1 from \sqrt2 which means you are doing an extra needless calculation which you've already covered. Check it.
    Did it again

    I don't know how to workout the 2nd bracket the one with a negative surd



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    (Original post by z_o_e)
    Did it again

    I don't know how to workout the 2nd bracket the one with a negative surd



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    In the same way you worked out \sqrt3 \cdot 2 just, well, it's a negative quantity this time.
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    (Original post by RDKGames)
    In the same way you worked out \sqrt3 \cdot 2 just, well, it's a negative quantity this time.
    Correct?

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    How should I add them now ? :/



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    (Original post by z_o_e)
    How should I add them now ? :/



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    Yeppp. Add what???
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    (Original post by RDKGames)
    Yeppp. Add what???
    You know when I have to work out the next step I need to add these right?


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    (Original post by z_o_e)
    You know when I have to work out the next step I need to add these right?


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    Yeah you would only add them if they shared any common terms. In this case they are all individual so you don't.

    If there was something like \sqrt3 + 1 + 7\sqrt3 - \sqrt2 then you can add the \sqrt3 and 7\sqrt3 (which would gives you 8\sqrt3) because \sqrt3 is a common term amongst those two numbers.
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    Oh okay

    So what do I do next?

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    (Original post by z_o_e)
    Oh okay

    So what do I do next?

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    You can leave the answer as it is since you cannot simplify it any further.

    Have a go at the question I've proposed earlier.
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    (Original post by RDKGames)
    You can leave the answer as it is since you cannot simplify it any further.

    Have a go at the question I've proposed earlier.
    Yep I will can I have a bit of an explanation to how to do that whilst I do another example to this x

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    (Original post by RDKGames)
    You can leave the answer as it is since you cannot simplify it any further.

    Have a go at the question I've proposed earlier.
    What do I do after this step?


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    (Original post by z_o_e)
    Yep I will can I have a bit of an explanation to how to do that whilst I do another example to this x

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    Well the explanation would come from you attempting to rationalise the denominator there by getting rid off the \sqrt3.

    Hint:
    Spoiler:
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    Multiply 2+\sqrt3 by 2+\sqrt3 and see what happens.
    Now separately multiply 2+\sqrt3 by 2-\sqrt3 and see if that helps you more than the previous result.

    Once you see which result gives you the rationalised expression, you know what to multiply the numerator and denominator of \frac{1}{2+\sqrt3} by.
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    (Original post by z_o_e)
    What do I do after this step?


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    You got the part with 2\sqrt{45} + 18 right and you know that \sqrt{45}=3\sqrt5 from what you've shown. You can use this replace the \sqrt{45} in the original answer.
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    (Original post by RDKGames)
    Well the explanation would come from you attempting to rationalise the denominator there by getting rid off the \sqrt3.

    Hint:
    Spoiler:
    Show
    Multiply 2+\sqrt3 by 2+\sqrt3 and see what happens.
    Now separately multiply 2+\sqrt3 by 2-\sqrt3 and see if that helps you more than the previous result.

    Once you see which result gives you the rationalised expression, you know what to multiply the numerator and denominator of \frac{1}{2+\sqrt3} by.
    Here


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