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

- Jamierox4ev3r

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

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- jamiebookeater

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- Jamierox4ev3r

Give me a second while I type out the expression. Thank you

- Jamierox4ev3r

\(\huge\frac{\sqrt{10}}{\sqrt{5}-2}\)

- anonymous

do you know the root of ten?

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## More answers

- Jamierox4ev3r

yes. The root of 10 is not rational, so I don't see how knowing that would help me solve this problem

- Jamierox4ev3r

\(\huge\sqrt{10} = 3.16227766...\)

- Jamierox4ev3r

I have a very limited recollection on rationalizing. So an explanation on that would be nice as well, thank you

- 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

do you want to see if you can do anything by multiplying it by a conjugate

- Jamierox4ev3r

a conjugate...so like the opposite? do you mean multiplying by \(\huge\sqrt{5}+2\) ??

- Jamierox4ev3r

o-o

- anonymous

|dw:1440462611069:dw|

- 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

root of 30 is irrational

- 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

is that denominator \(\huge \sqrt{5}-2~ or~ \sqrt{5-2}\)

- Jamierox4ev3r

wait lemme check mein textbook

- Jamierox4ev3r

it is definitely \(\huge\sqrt{5}-2\)

- 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

|dw:1440462940673:dw|

- 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

oh right! inverses :S

- anonymous

all i can say is that your answer will always be irrational so you have to work your way through the roots

- nincompoop

let me show you another example
\((\sqrt{2} +3) \times (\sqrt{2}-3) = 2-9 = 7 \)

- nincompoop

oops -7 not 7 haha

- Jamierox4ev3r

right, so there wouldn't be a root over the two any more

- Jamierox4ev3r

I recall that rule: \[\sqrt{x^{2}}\] = x

- nincompoop

see the cool stuff multiplying by conjugate does? it gives you a whole new other possibilities such as rationalizing your denominator

- Jamierox4ev3r

i see i see.

- anonymous

you could do|dw:1440463196135:dw|

- Jamierox4ev3r

how would you multiply on the numerator though?

- anonymous

ur answer is 2root10 plus 5root2

- nincompoop

you multiply it like any root multiplication
\(\sqrt{2} \times \sqrt{5} = \sqrt{2 \times 5} =\sqrt{10} \)

- anonymous

@nincompoop ur making it way harder than it is

- nincompoop

\(\sqrt{5} \times \sqrt{10} = \sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5 \sqrt{2} \)

- anonymous

heres the answer \[2\sqrt{10}+5\sqrt{2}\]

- Jamierox4ev3r

Oh I see. so you basically simplified \(\sqrt{50}\) Down to \(5\sqrt{2}\). I understand that

- nincompoop

yeeeeee
now try your own problem

- Jamierox4ev3r

as for the \(2\sqrt{10}\), that's just 2 x \(\sqrt{10}\). Got it!

- nincompoop

Do not pay attention to those people that only give you answers. Those kind of people do not encourage intellectual growth.

- anonymous

well you make everything way harder than it already is

- 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

*nin
oops my bad

- anonymous

i'd just help the person that let him get an F

- anonymous

*than

- Jamierox4ev3r

*then
and that's not a good philosophy

- 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

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

in fact, getting temporarily "bailed out" will actually damage you in the long run. hoo boy let me tell ya

- nincompoop

enough bs in the thread. move on to the next question

- 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

if u guys have a problem then deal with it because someone broke my hand because i didn't give him an answer

- anonymous

scru dis

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