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1. 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
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
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
From there you could rationalise.

But the easiest way to do this is to start again and use the fact that
4. (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

This is akin to when we have - common denominators.

Back to the point: we have we want to rationalise this, so we'll multiply top and bottom by to get us:

5. (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
Isn't that what he's done? It's how he got , isn't it? I can't quite see a simpler way except to pull out a factor of .
6. How can I put the numbers like that?
7. (Original post by Zacken)
Isn't that what he's done? It's how he got , isn't it? I can't quite see a simpler way except to pull out a factor of .
It's easy to show

And then simplify to get it in the form a + b root c.
8. (Original post by notnek)
It's easy to show

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.
9. (Original post by Zacken)
So we have

This is akin to when we have - common denominators.

Back to the point: we have we want to rationalise this, so we'll multiply top and bottom by to get us:

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.
10. (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.
11. (Original post by Zacken)
That's what he's done though - if I'm not mistaken.

It's inconsequential anyway, nevermind.
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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