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help with fractional surds.

hi so im kicking myself because i know this question is easy but im just not getting it, i have searched for help and what i have found has just confused me further.

i need to express root 1/2 + root 1/4 + root 1/8 as a + b root c

so far i have gotten to 1/root 2 + 1/2 + 1/(2 root 2) but the process of turning 1/root 2 + 1/(2 root 2) into 3/4 root 2 is evading me

can any of you illustrate that last step for me please
Original post by Henry27
hi so im kicking myself because i know this question is easy but im just not getting it, i have searched for help and what i have found has just confused me further.

i need to express root 1/2 + root 1/4 + root 1/8 as a + b root c

so far i have gotten to 1/root 2 + 1/2 + 1/(2 root 2) but the process of turning 1/root 2 + 1/(2 root 2) into 3/4 root 2 is evading me

can any of you illustrate that last step for me please


Please, post your workings.
Reply 2
Original post by Henry27
hi so im kicking myself because i know this question is easy but im just not getting it, i have searched for help and what i have found has just confused me further.

i need to express root 1/2 + root 1/4 + root 1/8 as a + b root c

so far i have gotten to 1/root 2 + 1/2 + 1/(2 root 2) but the process of turning 1/root 2 + 1/(2 root 2) into 3/4 root 2 is evading me

can any of you illustrate that last step for me please

From there you could rationalise.

But the easiest way to do this is to start again and use the fact that 18=12×14\displaystyle \frac{1}{8} = \frac{1}{2} \times \frac{1}{4}
Reply 3
Original post by Henry27
hi so im kicking myself because i know this question is easy but im just not getting it, i have searched for help and what i have found has just confused me further.

i need to express root 1/2 + root 1/4 + root 1/8 as a + b root c

so far i have gotten to 1/root 2 + 1/2 + 1/(2 root 2) but the process of turning 1/root 2 + 1/(2 root 2) into 3/4 root 2 is evading me

can any of you illustrate that last step for me please


So we have 12+122=222+122=322\displaystyle \frac{1}{\sqrt{2}} + \frac{1}{2\sqrt{2}} = \frac{2}{2\sqrt{2}} + \frac{1}{2\sqrt{2}} = \frac{3}{2\sqrt{2}}

This is akin to when we have 12+14=24+14=34\frac{1}{2} + \frac{1}{4} = \frac{2}{4} + \frac{1}{4} = \frac{3}{4} - common denominators.

Back to the point: we have 322\displaystyle \frac{3}{2\sqrt{2}} we want to rationalise this, so we'll multiply top and bottom by 2\sqrt{2} to get us:

322×22=32222=322×2\displaystyle \frac{3}{2\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{3\sqrt{2}}{2\sqrt{2}\sqrt{2}} = \frac{3\sqrt{2}}{2\times 2}
Reply 4
Original post by notnek
From there you could rationalise.

But the easiest way to do this is to start again and use the fact that 18=12×14\displaystyle \frac{1}{8} = \frac{1}{2} \times \frac{1}{4}


Isn't that what he's done? It's how he got 18=122\frac{1}{\sqrt{8}} = \frac{1}{2\sqrt{2}}, isn't it? I can't quite see a simpler way except to pull out a factor of 12\frac{1}{\sqrt{2}}.
Reply 5
How can I put the numbers like that?
Reply 6
Original post by Zacken
Isn't that what he's done? It's how he got 18=122\frac{1}{\sqrt{8}} = \frac{1}{2\sqrt{2}}, isn't it? I can't quite see a simpler way except to pull out a factor of 12\frac{1}{\sqrt{2}}.

It's easy to show 18=1212\sqrt{\frac{1}{8}} = \frac{1}{2}\sqrt{\frac{1}{2}}

And then simplify to get it in the form a + b root c.
Reply 7
Original post by notnek
It's easy to show 18=1212\sqrt{\frac{1}{8}} = \frac{1}{2}\sqrt{\frac{1}{2}}

And then simplify to get it in the form a + b root c.



That's what he's done though - if I'm not mistaken.

Original post by Henry27

so far i have gotten to 1/root 2 + 1/2 + 1/(2 root 2) but the process of turning 1/root 2 + 1/(2 root 2) into 3/4 root 2 is evading me


It's inconsequential anyway, nevermind. :lol:
Reply 8
Original post by Zacken
So we have 12+122=222+122=322\displaystyle \frac{1}{\sqrt{2}} + \frac{1}{2\sqrt{2}} = \frac{2}{2\sqrt{2}} + \frac{1}{2\sqrt{2}} = \frac{3}{2\sqrt{2}}

This is akin to when we have 12+14=24+14=34\frac{1}{2} + \frac{1}{4} = \frac{2}{4} + \frac{1}{4} = \frac{3}{4} - common denominators.

Back to the point: we have 322\displaystyle \frac{3}{2\sqrt{2}} we want to rationalise this, so we'll multiply top and bottom by 2\sqrt{2} to get us:

322×22=32222=322×2\displaystyle \frac{3}{2\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{3\sqrt{2}}{2\sqrt{2}\sqrt{2}} = \frac{3\sqrt{2}}{2\times 2}


that is absolutely perfect, in fact now i see it i cant actually work out where i was going wrong haha.

thanks for the help guys.
Reply 9
Original post by Henry27
that is absolutely perfect, in fact now i see it i cant actually work out where i was going wrong haha.

thanks for the help guys.


Glad it helped! :biggrin:
Reply 10
Original post by Zacken
That's what he's done though - if I'm not mistaken.



It's inconsequential anyway, nevermind. :lol:

I assumed a + b root c meant for any a, b, c - the question wasn't clear. Then rationalising would be unnecessary.

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