C1 MATHS HELP: Surds - Where did I go wrong?

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creativebuzz
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This is my working:

2/r3 – r6/r72

=2/r3 – r6/3r8

=6r8-r18/3r24

=6(2 x r2) – (3r2)/3r24

=12r2 – 3r2/3(2r6)

=9r2/6r6

=3r2/2r6

=3r2/2r3 x r2

=3/2r2

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BobLoblawLawBlog
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(Original post by creativebuzz)
This is my working:

2/r3 – r6/r72

=2/r3 – r6/3r8

=6r8-r18/3r24

=6(2 x r2) – (3r2)/3r24

=12r2 – 3r2/3(2r6)

=9r2/6r6

=3r2/2r6

=3r2/2r3 x r2

=3/2r2

Image
That seems correct to me. Although I'm guessing they probably want you to rationalise the denominator on your final answer.

Also, it may have been a bit quicker if you simplified each fraction further before expressing it as a single fraction. (e.g. \sqrt{72} = 6\sqrt{2}).
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creativebuzz
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(Original post by brittanna)
That seems correct to me. Although I'm guessing they probably want you to rationalise the denominator on your final answer.

Also, it may have been a bit quicker if you simplified each fraction further before expressing it as a single fraction. (e.g. \sqrt{72} = 6\sqrt{2}).
I appreciate that I should have simplified earlier on but, even if I didn't and if everything I did in my working out was mathematically correct, why did I not get 1/2r3 (the correct answer) as my end result? :/
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BobLoblawLawBlog
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(Original post by creativebuzz)
I appreciate that I should have simplified earlier on but, even if I didn't and if everything I did in my working out was mathematically correct, why did I not get 1/2r3 (the correct answer) as my end result? :/
You made a small mistake in the very last line. You should have \sqrt{3} there rather than \sqrt{2}.

Are you sure the answer is definitely \frac{1}{2\sqrt{3}}? As I'm getting \frac{3}{2\sqrt{3}} as the answer, which is what you'll get when you correct that small mistake.
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creativebuzz
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(Original post by brittanna)
You made a small mistake in the very last line. You should have \sqrt{3} there rather than \sqrt{2}.

Are you sure the answer is definitely \frac{1}{2\sqrt{3}}? As I'm getting \frac{3}{2\sqrt{3}} as the answer, which is what you'll get when you correct that small mistake.
Oh yeah, I see that now! I thought it was that too but according to the Soloman Answer sheet, this is the answer:
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Magnesium
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(Original post by creativebuzz)
Oh yeah, I see that now! I thought it was that too but according to the Soloman Answer sheet, this is the answer:
Image
You could also do it a different way by rationalising the denominator on both surds, making both denominators equal to 24 and you get r3/2 - same as the answer sheet

ie. 2/r3 - r6/r72
= 2/r3 - r6/3r8
= 2r3/3 - r48/24
= 16r3/24 - 4r3/24
= 12r3/24
= 1/2 r3
= r3/2

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BobLoblawLawBlog
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(Original post by creativebuzz)
Oh yeah, I see that now! I thought it was that too but according to the Soloman Answer sheet, this is the answer:
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Yeah, this is correct. This is because \displaystyle\frac{3}{2\sqrt{3}} * \frac{\sqrt{3}}{\sqrt{3}} = \frac{\sqrt{3}}{2}.
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creativebuzz
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(Original post by brittanna)
Yeah, this is correct. This is because \displaystyle\frac{3}{2\sqrt{3}} * \frac{\sqrt{3}}{\sqrt{3}} = \frac{\sqrt{3}}{2}.
So where did I go wrong in my working out (except for the last line issue)
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BobLoblawLawBlog
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(Original post by creativebuzz)
So where did I go wrong in my working out (except for the last line issue)
You didn't, you just have the square root on the bottom, and they have it on the top. They're the same answer.
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creativebuzz
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(Original post by brittanna)
You didn't, you just have the square root on the bottom, and they have it on the top. They're the same answer.
Oh yeaah! Thank god, I kept going over it think I made a mistake somewhere in between
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