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<a https://www.thestudentroom.co.uk/showthread.php?t=7467335'> Year 12s: what will be the first way you research your future options? >>
<a https://www.thestudentroom.co.uk/showthread.php?t=7467335'> Year 12s: what will be the first way you research your future options? >>
<a https://www.thestudentroom.co.uk/showthread.php?t=7467335'> Year 12s: what will be the first way you research your future options? >>

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Surds

Hi :smile:

In the question :

'write root 18 + 8/ root 2 in the form a+b root 2 where a and b are integers'.

I get the answer as 3+ 4 root 2

I was wondering is it possible to simplify the answer so it becomes 3+2 root 2? Or is that just wrong?

Thanks.
Reply 1
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nuodai
17
Is it 18+82\sqrt{18} + \dfrac{8}{\sqrt{2}}? If so, I don't agree with either answer; I think it should be 727\sqrt{2}.

You can't simplify 3+423 + 4\sqrt{2} to get 3+223 + 2\sqrt{2}. Suppose it is true, then:
3+42=3+223 + 4\sqrt{2} = 3 + 2\sqrt{2}
⇒42=22\Rightarrow 4\sqrt{2} = 2\sqrt{2}
⇒22=0\Rightarrow 2\sqrt{2} = 0
(...which definitely isn't right!)
Shehz94
'write root 18 + 8/ root 2 in the form a+b root 2 where a and b are integers'.

Sqrt18 + 8/Sqrt2 = (Sqrt36 + 8)/Sqrt2 = 14/Sqrt2 = 7Sqrt2

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