Jamierox4ev3r
  • Jamierox4ev3r
Math Review Day 2! 6a. Rationalize the expression and simplify
Mathematics
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jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
Jamierox4ev3r
  • Jamierox4ev3r
Give me a second while I type out the expression. Thank you
Jamierox4ev3r
  • Jamierox4ev3r
\(\huge\frac{\sqrt{10}}{\sqrt{5}-2}\)
anonymous
  • anonymous
do you know the root of ten?

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Jamierox4ev3r
  • Jamierox4ev3r
yes. The root of 10 is not rational, so I don't see how knowing that would help me solve this problem
Jamierox4ev3r
  • Jamierox4ev3r
\(\huge\sqrt{10} = 3.16227766...\)
Jamierox4ev3r
  • Jamierox4ev3r
I have a very limited recollection on rationalizing. So an explanation on that would be nice as well, thank you
anonymous
  • anonymous
i learned that you can use a perfect number to minimalize something like this heres an example the root of 18 equals 3root2
nincompoop
  • nincompoop
do you want to see if you can do anything by multiplying it by a conjugate
Jamierox4ev3r
  • Jamierox4ev3r
a conjugate...so like the opposite? do you mean multiplying by \(\huge\sqrt{5}+2\) ??
Jamierox4ev3r
  • Jamierox4ev3r
o-o
anonymous
  • anonymous
|dw:1440462611069:dw|
nincompoop
  • nincompoop
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.
anonymous
  • anonymous
root of 30 is irrational
Jamierox4ev3r
  • Jamierox4ev3r
okay.... but what would that accomplish? you're not really getting rid of the denominator by doing that, at least i don't think
nincompoop
  • nincompoop
is that denominator \(\huge \sqrt{5}-2~ or~ \sqrt{5-2}\)
Jamierox4ev3r
  • Jamierox4ev3r
wait lemme check mein textbook
Jamierox4ev3r
  • Jamierox4ev3r
it is definitely \(\huge\sqrt{5}-2\)
nincompoop
  • nincompoop
Then try multiplying by conjugate and see what it will yield. you will find out if it will do anything cool or not
anonymous
  • anonymous
|dw:1440462940673:dw|
nincompoop
  • nincompoop
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?
Jamierox4ev3r
  • Jamierox4ev3r
oh right! inverses :S
anonymous
  • anonymous
all i can say is that your answer will always be irrational so you have to work your way through the roots
nincompoop
  • nincompoop
let me show you another example \((\sqrt{2} +3) \times (\sqrt{2}-3) = 2-9 = 7 \)
nincompoop
  • nincompoop
oops -7 not 7 haha
Jamierox4ev3r
  • Jamierox4ev3r
right, so there wouldn't be a root over the two any more
Jamierox4ev3r
  • Jamierox4ev3r
I recall that rule: \[\sqrt{x^{2}}\] = x
nincompoop
  • nincompoop
see the cool stuff multiplying by conjugate does? it gives you a whole new other possibilities such as rationalizing your denominator
Jamierox4ev3r
  • Jamierox4ev3r
i see i see.
anonymous
  • anonymous
you could do|dw:1440463196135:dw|
Jamierox4ev3r
  • Jamierox4ev3r
how would you multiply on the numerator though?
anonymous
  • anonymous
ur answer is 2root10 plus 5root2
nincompoop
  • nincompoop
you multiply it like any root multiplication \(\sqrt{2} \times \sqrt{5} = \sqrt{2 \times 5} =\sqrt{10} \)
anonymous
  • anonymous
@nincompoop ur making it way harder than it is
nincompoop
  • nincompoop
\(\sqrt{5} \times \sqrt{10} = \sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5 \sqrt{2} \)
anonymous
  • anonymous
heres the answer \[2\sqrt{10}+5\sqrt{2}\]
Jamierox4ev3r
  • Jamierox4ev3r
Oh I see. so you basically simplified \(\sqrt{50}\) Down to \(5\sqrt{2}\). I understand that
nincompoop
  • nincompoop
yeeeeee now try your own problem
Jamierox4ev3r
  • Jamierox4ev3r
as for the \(2\sqrt{10}\), that's just 2 x \(\sqrt{10}\). Got it!
nincompoop
  • nincompoop
Do not pay attention to those people that only give you answers. Those kind of people do not encourage intellectual growth.
anonymous
  • anonymous
well you make everything way harder than it already is
Jamierox4ev3r
  • Jamierox4ev3r
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)
Jamierox4ev3r
  • Jamierox4ev3r
*nin oops my bad
anonymous
  • anonymous
i'd just help the person that let him get an F
anonymous
  • anonymous
*than
Jamierox4ev3r
  • Jamierox4ev3r
*then and that's not a good philosophy
nincompoop
  • nincompoop
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.
anonymous
  • anonymous
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
Jamierox4ev3r
  • Jamierox4ev3r
in fact, getting temporarily "bailed out" will actually damage you in the long run. hoo boy let me tell ya
nincompoop
  • nincompoop
enough bs in the thread. move on to the next question
Jamierox4ev3r
  • Jamierox4ev3r
Anyhow, I'm closing this. Thank you for your thorough explanation @nincompoop and @GTA_Hunter35 try not to provide answers in the future. Thanks
anonymous
  • anonymous
if u guys have a problem then deal with it because someone broke my hand because i didn't give him an answer
anonymous
  • anonymous
scru dis

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