Math Review Day 2! 6a. Rationalize the expression and simplify

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Math Review Day 2! 6a. Rationalize the expression and simplify

Mathematics
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Give me a second while I type out the expression. Thank you
\(\huge\frac{\sqrt{10}}{\sqrt{5}-2}\)
do you know the root of ten?

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yes. The root of 10 is not rational, so I don't see how knowing that would help me solve this problem
\(\huge\sqrt{10} = 3.16227766...\)
I have a very limited recollection on rationalizing. So an explanation on that would be nice as well, thank you
i learned that you can use a perfect number to minimalize something like this heres an example the root of 18 equals 3root2
do you want to see if you can do anything by multiplying it by a conjugate
a conjugate...so like the opposite? do you mean multiplying by \(\huge\sqrt{5}+2\) ??
o-o
|dw:1440462611069:dw|
yes, so in effect if you multiply your original expression by \(\huge \frac{\sqrt{5}+2}{\sqrt{5}+2} \) you are in effect multiplying by 1, which does not change the original expression.
root of 30 is irrational
okay.... but what would that accomplish? you're not really getting rid of the denominator by doing that, at least i don't think
is that denominator \(\huge \sqrt{5}-2~ or~ \sqrt{5-2}\)
wait lemme check mein textbook
it is definitely \(\huge\sqrt{5}-2\)
Then try multiplying by conjugate and see what it will yield. you will find out if it will do anything cool or not
|dw:1440462940673:dw|
what happens when you multiply a binomial expression by its conjugate? let me show you an example \((a+b) \times (a-b) = a^2-b^2 \) you lose the middle term in a typical trinomial giving you binomial expression still. Here's the fun part, what does the squared term does to a square root?
oh right! inverses :S
all i can say is that your answer will always be irrational so you have to work your way through the roots
let me show you another example \((\sqrt{2} +3) \times (\sqrt{2}-3) = 2-9 = 7 \)
oops -7 not 7 haha
right, so there wouldn't be a root over the two any more
I recall that rule: \[\sqrt{x^{2}}\] = x
see the cool stuff multiplying by conjugate does? it gives you a whole new other possibilities such as rationalizing your denominator
i see i see.
you could do|dw:1440463196135:dw|
how would you multiply on the numerator though?
ur answer is 2root10 plus 5root2
you multiply it like any root multiplication \(\sqrt{2} \times \sqrt{5} = \sqrt{2 \times 5} =\sqrt{10} \)
@nincompoop ur making it way harder than it is
\(\sqrt{5} \times \sqrt{10} = \sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5 \sqrt{2} \)
heres the answer \[2\sqrt{10}+5\sqrt{2}\]
Oh I see. so you basically simplified \(\sqrt{50}\) Down to \(5\sqrt{2}\). I understand that
yeeeeee now try your own problem
as for the \(2\sqrt{10}\), that's just 2 x \(\sqrt{10}\). Got it!
Do not pay attention to those people that only give you answers. Those kind of people do not encourage intellectual growth.
well you make everything way harder than it already is
so lol hunter you were right. Sorry, I liked how nine explained better. and yeah nin, i know. I like to reach an understanding, I think that's vital for my learning (or in this case, review)
*nin oops my bad
i'd just help the person that let him get an F
*than
*then and that's not a good philosophy
get an F and learn your lesson and try HARDER next time... being bailed out does not necessarily mean helping that person understand anything, because you may just be compounding the lack of skills that should have been developed to proceed to the next level.
i already had this thing during my whole life: they said its my fault that they got an F and i got beat up for it
in fact, getting temporarily "bailed out" will actually damage you in the long run. hoo boy let me tell ya
enough bs in the thread. move on to the next question
Anyhow, I'm closing this. Thank you for your thorough explanation @nincompoop and @GTA_Hunter35 try not to provide answers in the future. Thanks
if u guys have a problem then deal with it because someone broke my hand because i didn't give him an answer
scru dis

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