## Callisto 3 years ago Tutor question #1 Simplify the following: $\frac{1}{\sqrt2 + \sqrt3 + \sqrt5}$ (conditions: pen, paper, no calculator, done in 2 minutes) *

1. Callisto

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

2. RaphaelFilgueiras

yes

3. apoorvk

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

4. Callisto

But it looks so messy...

5. bronzegoddess

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

6. Callisto

That's what rationalise means

7. apoorvk

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

8. bronzegoddess

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

9. Callisto

Can you correct it?

10. bronzegoddess

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

11. Callisto

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}$

12. RaphaelFilgueiras

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

13. bronzegoddess

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?

14. Callisto

see the first part of it..

15. RaphaelFilgueiras

5-5+2sqrt(6)*

16. RaphaelFilgueiras

second line

17. Callisto

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

18. bronzegoddess

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

19. Callisto

Of course! That's 'rationalise'

20. bronzegoddess

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

21. RaphaelFilgueiras

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

22. Callisto

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

23. Callisto

Do you mind re-type it again?

24. RaphaelFilgueiras

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

25. Callisto

Okay, and the answer is the same?

26. RaphaelFilgueiras

yes

27. Callisto

Okay, thanks everyone!!!