Thread: Fractions in surds

1. Fractions in surds

Hi,

Hope you guys can help... the question is as follows.

How do I represent:

√1/2 + √1/4 + √1/8

as....

a + b √c

I think you can take it to:

√1/ √2 + √1/ √4 + √1/8..... but does that actually help me?!

The steps of what you did would be greatly appreciated!

ajkerr

2. Originally Posted by ajkerr
Hi,

Hope you guys can help... the question is as follows.

How do I represent:

√1/2 + √1/4 + √1/8

as....

a + b √c

I think you can take it to:

√1/ √2 + √1/ √4 + √1/8..... but does that actually help me?!

The steps of what you did would be greatly appreciated!

ajkerr
it does help. simplify each term as much as possible, then find the sum. if there is something without radical signs, leave it by itself and sum the things with radicals

3. But surely I have to have a common denominator to add them at the end and I wouldn't if I simplified them as I would get √2, 2 and then 2 √2?!

Uh?!

4. Originally Posted by ajkerr
Hi,

Hope you guys can help... the question is as follows.

How do I represent:

√1/2 + √1/4 + √1/8

as....

a + b √c

I think you can take it to:

√1/ √2 + √1/ √4 + √1/8..... but does that actually help me?!

The steps of what you did would be greatly appreciated!

ajkerr
$\sqrt{\frac{1}{2}}=\frac{1}{\sqrt {2}}$

$=\frac{1}{\sqrt {2}} \times \frac{\sqrt{2}}{\sqrt{2}}=\frac{\sqrt{2}}{2}$

Now you try to simplify further.

for adding, make the denominator same of each term.

5. Originally Posted by Shyam
$\sqrt{\frac{1}{2}}=\frac{1}{\sqrt {2}}$

$=\frac{1}{\sqrt {2}} \times \frac{\sqrt{2}}{\sqrt{2}}=\frac{\sqrt{2}}{2}$

Now you try to simplify further.
soo.....

then √1/4 = 1/ √4

and then..... 1/ √4 x √4/ √4 = √4/4

then √1/8 = 1/ √8

and then 1/ √8 x √8/ √8 = √8/8

leaving me with...

√2 /2 + √4 /4+ √8 /8

denominator to...

4√2 / 8 + 2√4 / 8 + 8√8 to get (4√2+2√4+8√8) / 8 -- is that right?

then what?

6. Originally Posted by ajkerr
soo.....

then √1/4 = 1/ √4

and then..... 1/ √4 x √4/ √4 = √4/4

then √1/8 = 1/ √8

and then 1/ √8 x √8/ √8 = √8/8

leaving me with...

√2 /2 + √4 /4+ √8 /8

and then do I times them up to get a common denominator?
you realize $\sqrt{4} = 2$, right?

so you have $\frac 12 + \frac {\sqrt{2}}2 + \frac {\sqrt{8}}8$

now add the last two fractions

7. Originally Posted by Jhevon
you realize $\sqrt{4} = 2$

so you have $\frac 12 + \frac {\sqrt{2}}2 + \frac {\sqrt{8}}8$

now add the last two fractions

Doh! -- I knew that really.... err! Ok thanks

So

1/2 + √2/2 + √8/8

to make....

1/2 + 4 √2/8 + √8/8 = 1/2 + 3/4 √2

So the answer should be...

1/2 + 3/4 √2

I think.....

8. Originally Posted by ajkerr
Doh! -- I knew that really.... err! Ok thanks

So

1/2 + √2/2 + √8/8

to make....

1/2 + 4 √2/8 + √8/8 = 1/2 + 3/4 √2

So the answer should be...

1/2 + (3/4) √2

I think.....
yes

9. "Ahh finally" they all say "he's got it!"

Thanks so much... one of those questions that really bugs you!

Thanks again

Ajk

10. Originally Posted by ajkerr
"Ahh finally" they all say "he's got it!"

Thanks so much... one of those questions that really bugs you!

Thanks again

Ajk
yeah, you have those sometimes. but it wasn't so bad, was it?

11. $\sqrt{8}$ can and should be simplified further.

$\sqrt{\frac{1}{2}} + \sqrt{\frac{1}{4}} + \sqrt{\frac{1}{8}} = \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{4}} + \frac{1}{\sqrt{8}}$

$= \frac{\sqrt{2}}{2} + \frac{1}{2} + \frac{\sqrt{8}}{8}$

$= \frac{1+\sqrt{2}}{2} + \frac{2 \sqrt{2}}{8}$

$= \frac{2 + 2\sqrt{2}}{4} + \frac{\sqrt{2}}{4}$

$= \frac{2 + 3\sqrt{2}}{4}$.

12. Originally Posted by Prove It
$\sqrt{8}$ can and should be simplified further.

$\sqrt{\frac{1}{2}} + \sqrt{\frac{1}{4}} + \sqrt{\frac{1}{8}} = \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{4}} + \frac{1}{\sqrt{8}}$

$= \frac{\sqrt{2}}{2} + \frac{1}{2} + \frac{\sqrt{8}}{8}$

$= \frac{1+\sqrt{2}}{2} + \frac{2 \sqrt{2}}{8}$

$= \frac{2 + 2\sqrt{2}}{4} + \frac{\sqrt{2}}{4}$

$= \frac{2 + 3\sqrt{2}}{4}$.
that is what the poster got. he just wrote it in the form $a + b \sqrt{c}$ as he was directed