Question

Tutor question #1
Simplify the following:
\[\frac{1}{\sqrt2 + \sqrt3 + \sqrt5}\]
(conditions: pen, paper, no calculator, done in 2 minutes)
*

Answer 1

I got \[ \frac{2\sqrt3 + 3\sqrt2 - \sqrt{30}}{12}\] Was that right?

Answer 2

yes

Answer 3

HUNDRED PERCENT!!!!!!!!!!!!!

Answer 4

But it looks so messy...

Answer 5

i got something different: isn't it you cant have radicals under a fraction so you multiply by the conjugate?

Answer 6

That's what rationalise means

Answer 7

Not messy at all, this is the only way to go about it.

Answer 8

yes but if you multiply 1 by the conjugate pair you get the conjugate pair.. your numerator seems wrong..

Answer 9

Can you correct it?

Answer 10

otherwise can someone please show me a step by step to how you got that answer? and i'll show you what i did :)

Answer 11

luckily, I haven't deleted that..
\[(\sqrt2 + \sqrt3 + \sqrt5)(\sqrt2 + \sqrt3 - \sqrt5)\]\[ = (\sqrt2 + \sqrt3)^2-5\]\[ = 2 + 3 + 2\sqrt6-5\]\[=2\sqrt6\]
\[\frac{1}{\sqrt2 + \sqrt3 + \sqrt5}\]\[ = \frac{\sqrt2 + \sqrt3 - \sqrt5}{(\sqrt2 + \sqrt3 + \sqrt5)(\sqrt2 + \sqrt3 - \sqrt5)}\]\[ = \frac{\sqrt2 + \sqrt3 - \sqrt5}{2\sqrt6}\]\[ = \frac{2\sqrt3 + 3\sqrt2 - \sqrt{30}}{12}\]

Answer 12

\[1/(\sqrt{2}+\sqrt{3}+\sqrt{5})=1/(a+\sqrt{5})=(a-sqrt{5})/(a^{2}-5)\]
\[(\sqrt{2}+\sqrt{3}-\sqrt{5})/(5-5+\sqrt{6})\]
\[\sqrt{2}+\sqrt{3}-\sqrt{5}/2\sqrt{6}=2.\sqrt{3}+2.\sqrt{2}-\sqrt{30}/12\]

Answer 13

I ended at the second to last step... where did you get the 2 in front of the radicals if you are multiplying by 1?

Answer 14

see the first part of it..

Answer 15

5-5+2sqrt(6)*

Answer 16

second line

Answer 17

@RaphaelFilgueiras The second term of the numerator is 3\sqrt{2} ?! \sqrt{18} = \sqrt{9 times 2} = 3\sqrt2 ...

Answer 18

okay, so the you rationalized the second to last line because of the radical at the bottom?

Answer 19

Of course! That's 'rationalise'

Answer 20

okay sorry, then you are right.. I just wanted to know where I went wrong...

Answer 21

no in my solution i put (5-5+sqrt(5))(WRONG) instead(5-5+2sqrt(5))

Answer 22

Sorry, but I don't know what you're doing.. No offense.

Answer 23

Do you mind re-type it again?

Answer 24

i did same as you,but call(a=sqrt(2)+sqrt(3))

Answer 25

Okay, and the answer is the same?

Answer 26

yes

Answer 27

Okay, thanks everyone!!!