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    (Original post by RDKGames)
    Remember your surd rules for multiplication and have a go. \sqrt{a} \cdot \sqrt{b} = \sqrt{ab} use this for the first one to try and get the answer of 4.
    How's this?



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    (Original post by z_o_e)
    How's this?



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    Correct. Simplify it further.
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    (Original post by RDKGames)
    Correct. Simplify it further.


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    I don't understand how you go from 2\sqrt4 to 2\sqrt2. Explain your thought process here.
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    (Original post by RDKGames)
    I don't understand how you go from 2\sqrt4 to 2\sqrt2. Explain your thought process here.
    Well I found what makes 4 and 2*2 makes four.

    Surd 2 and surd 2 cancels out and gives 2 so we can put that two as it's simplified inside the surd.

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    (Original post by z_o_e)
    Well I found what makes 4 and 2*2 makes four.

    Surd 2 and surd 2 cancels out and gives 2 so we can put that two as it's simplified inside the surd.

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    Nope. Root 2 and root 2 cancel to give 2, yes you're right, but you took the square root of 4 in the first place, the root is now gone as it cancels with the 2's, so where are you getting another root from that makes you put the 2 inside it?
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    (Original post by RDKGames)
    Nope. Root 2 and root 2 cancel to give 2, yes you're right, but you took the square root of 4 in the first place, the root is now gone as it cancels with the 2's, so where are you getting another root from that makes you put the 2 inside it?
    I'm really not sure.
    I have never covered surds. :/

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    (Original post by z_o_e)
    I'm really not sure.
    I have never covered surds. :/

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    Well that explains it. Watch this video to get the basics: https://www.youtube.com/watch?v=xpGlbt7Wg2U

    The one thing that the video doesn't explain is what a surd is by definition. A surd is an irrational number you get when you take the root an integer. This also means that surds cannot be expressed as fractions.
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    (Original post by RDKGames)
    Well that explains it. Watch this video to get the basics: https://www.youtube.com/watch?v=xpGlbt7Wg2U

    The one thing that the video doesn't explain is what a surd is by definition. A surd is an irrational number you get when you take the root an integer. This also means that surds cannot be expressed as fractions.
    Yep I took a look at it and that's the area simplifying which I don't understand

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    (Original post by z_o_e)
    Yep I took a look at it and that's the area simplifying which I don't understand

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    Give me an example from the video you don't understand and I'll walk you through it.
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    (Original post by RDKGames)
    Give me an example from the video you don't understand and I'll walk you through it.
    Yep I'm watching a video from maths solutions now.

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    (Original post by RDKGames)
    Give me an example from the video you don't understand and I'll walk you through it.
    I think you need to explain this


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    (Original post by z_o_e)
    I think you need to explain this


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    Okay there are several ways to think about it:

    One way
    If you list your square numbers from 1-10, you would get this:
    1^2=1

2^2=4

3^2=9

4^2=16

5^2=25

6^2=36

7^2=49

8^2=64

9^2=81

10^2=100

    As you can see, you have 5^2=25 in there which means that 25 is a square number. If you were to square root both sides (which is the reverse of squaring a number) you would get 5=\sqrt{25}

    Another way to think about it
    When you have a square root of a number, it is the same as raising that number to the power of 1/2. From this we can manipulate it using laws of indices and surd multiplication rule like so:

    \sqrt{25}=\sqrt{5\cdot 5}=\sqrt5 \cdot \sqrt5 = 5^{1/2} \cdot 5^{1/2} = (5^{1/2})^2 = 5^{2/2} = 5^1 = 5
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    (Original post by RDKGames)
    Okay there are several ways to think about it:

    One way
    If you list your square numbers from 1-10, you would get this:
    1^2=1

2^2=4

3^2=9

4^2=16

5^2=25

6^2=36

7^2=49

8^2=64

9^2=81

10^2=100

    As you can see, you have 5^2=25 in there which means that 25 is a square number. If you were to square root both sides (which is the reverse of squaring a number) you would get 5=\sqrt{25}

    Another way to think about it
    When you have a square root of a number, it is the same as raising that number to the power of 1/2. From this we can manipulate it using laws of indices and surd multiplication rule like so:

    \sqrt{25}=\sqrt{5\cdot 5}=\sqrt5 \cdot \sqrt5 = 5^{1/2} \cdot 5^{1/2} = (5^{1/2})^2 = 5^{2/2} = 5^1 = 5
    So where does the 12 go?


    So can we only simplify square numbers?


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    (Original post by z_o_e)
    So where does the 12 go?


    So can we only simplify square numbers?


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    That example was only for the root. After you simplify the root, and in this case you know that \sqrt{25}=5, you can replace the \sqrt{25} by 5.

    So you would go from 12(\sqrt{25}) to 12(5)

    (You can simplify non-squares too... don't get confused.)
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    (Original post by RDKGames)
    That example was only for the root. After you simplify the root, and in this case you know that \sqrt{25}=5, you can replace the \sqrt{25} by 5.

    So you would go from 12(\sqrt{25}) to 12(5)

    (You can simplify non-squares too... don't get confused.)
    For this question I got...

    The one on the white board is my Final answer after looking at your examples of simplifying. ..


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    (Original post by z_o_e)
    For this question I got...

    The one on the white board is my Final answer after looking at your examples of simplifying. ..


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    Yep, your surd manipulation looks solid now. However, one slight error you might've missed, 3\sqrt7 + 3\sqrt7 \not= 5\sqrt7 check that addition again. (also you can add 63 and 1, no point leaving them separate)
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    (Original post by RDKGames)
    Yep, your surd manipulation looks solid now. However, one slight error you might've missed, 3\sqrt7 + 3\sqrt7 \not= 5\sqrt7 check that addition again. (also you can add 63 and 1, no point leaving them separate)


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    (Original post by RDKGames)
    Yep, your surd manipulation looks solid now. However, one slight error you might've missed, 3\sqrt7 + 3\sqrt7 \not= 5\sqrt7 check that addition again. (also you can add 63 and 1, no point leaving them separate)
    How did this go?

    Shall I added 5 root 4 & root 6?



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