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

This Question is Closed

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.5I got \[ \frac{2\sqrt3 + 3\sqrt2  \sqrt{30}}{12}\] Was that right?

apoorvk
 2 years ago
Best ResponseYou've already chosen the best response.0HUNDRED PERCENT!!!!!!!!!!!!!

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.5But it looks so messy...

bronzegoddess
 2 years ago
Best ResponseYou've already chosen the best response.0i got something different: isn't it you cant have radicals under a fraction so you multiply by the conjugate?

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.5That's what rationalise means

apoorvk
 2 years ago
Best ResponseYou've already chosen the best response.0Not messy at all, this is the only way to go about it.

bronzegoddess
 2 years ago
Best ResponseYou've already chosen the best response.0yes but if you multiply 1 by the conjugate pair you get the conjugate pair.. your numerator seems wrong..

bronzegoddess
 2 years ago
Best ResponseYou've already chosen the best response.0otherwise can someone please show me a step by step to how you got that answer? and i'll show you what i did :)

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.5luckily, I haven't deleted that.. \[(\sqrt2 + \sqrt3 + \sqrt5)(\sqrt2 + \sqrt3  \sqrt5)\]\[ = (\sqrt2 + \sqrt3)^25\]\[ = 2 + 3 + 2\sqrt65\]\[=2\sqrt6\] \[\frac{1}{\sqrt2 + \sqrt3 + \sqrt5}\]\[ = \frac{\sqrt2 + \sqrt3  \sqrt5}{(\sqrt2 + \sqrt3 + \sqrt5)(\sqrt2 + \sqrt3  \sqrt5)}\]\[ = \frac{\sqrt2 + \sqrt3  \sqrt5}{2\sqrt6}\]\[ = \frac{2\sqrt3 + 3\sqrt2  \sqrt{30}}{12}\]

RaphaelFilgueiras
 2 years ago
Best ResponseYou've already chosen the best response.0\[1/(\sqrt{2}+\sqrt{3}+\sqrt{5})=1/(a+\sqrt{5})=(asqrt{5})/(a^{2}5)\] \[(\sqrt{2}+\sqrt{3}\sqrt{5})/(55+\sqrt{6})\] \[\sqrt{2}+\sqrt{3}\sqrt{5}/2\sqrt{6}=2.\sqrt{3}+2.\sqrt{2}\sqrt{30}/12\]

bronzegoddess
 2 years ago
Best ResponseYou've already chosen the best response.0I ended at the second to last step... where did you get the 2 in front of the radicals if you are multiplying by 1?

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.5see the first part of it..

RaphaelFilgueiras
 2 years ago
Best ResponseYou've already chosen the best response.055+2sqrt(6)*

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.5@RaphaelFilgueiras The second term of the numerator is 3\sqrt{2} ?! \sqrt{18} = \sqrt{9 times 2} = 3\sqrt2 ...

bronzegoddess
 2 years ago
Best ResponseYou've already chosen the best response.0okay, so the you rationalized the second to last line because of the radical at the bottom?

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.5Of course! That's 'rationalise'

bronzegoddess
 2 years ago
Best ResponseYou've already chosen the best response.0okay sorry, then you are right.. I just wanted to know where I went wrong...

RaphaelFilgueiras
 2 years ago
Best ResponseYou've already chosen the best response.0no in my solution i put (55+sqrt(5))(WRONG) instead(55+2sqrt(5))

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.5Sorry, but I don't know what you're doing.. No offense.

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.5Do you mind retype it again?

RaphaelFilgueiras
 2 years ago
Best ResponseYou've already chosen the best response.0i did same as you,but call(a=sqrt(2)+sqrt(3))

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.5Okay, and the answer is the same?

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.5Okay, thanks everyone!!!
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