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

1. Callisto Group Title

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

2. RaphaelFilgueiras Group Title

yes

3. apoorvk Group Title

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

4. Callisto Group Title

But it looks so messy...

5. bronzegoddess Group Title

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

6. Callisto Group Title

That's what rationalise means

7. apoorvk Group Title

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

8. bronzegoddess Group Title

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

9. Callisto Group Title

Can you correct it?

10. bronzegoddess Group Title

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 Group Title

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 Group Title

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

13. bronzegoddess Group Title

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 Group Title

see the first part of it..

15. RaphaelFilgueiras Group Title

5-5+2sqrt(6)*

16. RaphaelFilgueiras Group Title

second line

17. Callisto Group Title

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

18. bronzegoddess Group Title

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

19. Callisto Group Title

Of course! That's 'rationalise'

20. bronzegoddess Group Title

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

21. RaphaelFilgueiras Group Title

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

22. Callisto Group Title

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

23. Callisto Group Title

Do you mind re-type it again?

24. RaphaelFilgueiras Group Title

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

25. Callisto Group Title

Okay, and the answer is the same?

26. RaphaelFilgueiras Group Title

yes

27. Callisto Group Title

Okay, thanks everyone!!!