Root fractions

[restive otter]

Hello, can anyone explain how to solve a question like this one? I have a hard time with some of these exercises.
Thanks in advance.

[rare lichen]

adonhs

adonhs

adonhs

[restive otter]

Step 1 I have: sqrt(3^3)/sqrt(2^3)
Step 2: sqrt(3^2 * 3)/sqrt(2^2 *3)

[potent lava]

You can simply google the power rules

[potent lava]

nice

[restive otter]

Yes thanks. I know the power rules. But after step 2 I don't know.

[potent lava]

Split the root

[restive otter]

Because I came on an other answer as the answerbook

[rare lichen]

adonhs

[restive otter]

I did

[potent lava]

3^2 and 2^2 is very nice

[restive otter]

Thats sqrt(3^2) * 3 and sqrt(2^2) * 3

[potent lava]

no

sqrt(3) * 3

and sqrt(2^3) = sqrt(2^2 * 2)

not 2^2 * 3

and then sqrt(2^2) * sqrt(2)

[restive otter]

Huh yes I have that, wait ill try to illustrate.

[potent lava]

yea that's wrong the right

It should be

[rare lichen]

adonhs

[restive otter]

Okay thanks, is that the standard rule when you have a power of 3 or more?

[potent lava]

no the laws above are general

you just need to apply them correct

like

how come 2³ = 2² * 3???

[restive otter]

yes so standard?

[potent lava]

where does the 3 come from

yes

[restive otter]

Sorry men, I don't know. I just tried and thought like that.

[potent lava]

that's ok just trying to understand

the key is to find the root cause of mistakes 😄

[restive otter]

So, I know the correct answer but it doesn't make sense (yet) for me.

[potent lava]

they probably rationalized the denominator

[restive otter]

sqrt(3^2) should be 3 due to the answer but I honestly don't get that

[potent lava]

3^2 = 9

[restive otter]

Like isn't it sqrt(9)

yeah

[potent lava]

square root of 9 is 3

[restive otter]

9 I ean

Yes true

[potent lava]

you can also rewrite the root

[restive otter]

3 is correct

[rare lichen]

adonhs

[restive otter]

But why is sqrt(2^2) == 4?

[rare lichen]

adonhs

[potent lava]

2^2 = 4

[restive otter]

Not in the answerbook 😦

[potent lava]

square root of 4 is 2

well what is the result

[restive otter]

3/4 sqrt(6)

[rare lichen]

adonhs

[restive otter]

this answer

[restive otter]

Yes I understand

[potent lava]

Now notice

[restive otter]

these sqrt(3) is added to each other for 6

sqrt(6)

[potent lava]

It's common in math to rationalize the denominator

that means to get rid of any root in the denominator

it's just a convention

[rare lichen]

adonhs

[potent lava]

Now you will see the solution 🙂

It's called rationalizing the denominator

[restive otter]

Yes, I've saw this many times. I don't know why tbh.

[potent lava]

which is not really necessary but it is waht it is

it's a convention

hope u undertstand

[restive otter]

Ill try to see it now

[potent lava]

you should be able to now simplify

[restive otter]

I'm really sorry, but I don't know where you'd get that srt(2) on both sides from. Is it the last power^2 or what?

[potent lava]

because we wanna get rid of the root in the denominator

if you identify the root of the denominator it's sqrt(2)

[restive otter]

Ah ofcourse my bad.

[potent lava]

and we know sqrt(x) * sqrt(x) = x

this is what we want

so we extend the fractions with sqrt(2)/sqrt(2) legally

basically rewrite the thing "nicer"

the terms are still equal

it's like making 1/2 -> 2/4 by extending with 2/2

they are still both the same

[rare lichen]

adonhs

[wild turtle]

https://www.youtube.com/watch?v=EgYlGXnq8z8

[potent lava]

yes

[restive otter]

Oh wow thanks for the link. I'm gonna check it very soon. Firstly wanna understand the explanation from adonhs.

[potent lava]

i just tried to explain the steps, the actual reasoning behind rationalizing the denominator is to my knowledge a convention thing

[restive otter]

Okay, thank you. Coming back for this very soon. I saw the video is 6 minutes maybe it get me further in your explanation.

[potent lava]

as said, the video and me explaining the steps dont really correlate

the video explains the why and me the how

[restive otter]

Aahhh now I understand the concept much better, atleast, for this specific exercise. The other exercises should have the same framework/concept for solving it. I got to sharpen my English on math-level.

With that being said: i'll sum up from what i've learned/done the last idk 40/50 minutes.

1. Work out brackets
2. Make the power of 3 to power of 2 and multiply by that power with a root (3,2)
3. Than both the power roots simplify root(3^2) = 3 and root(2^2) = 2
4. Rationalize the denominator both by root(2)
5. Simplify the root(4) underneath because obviously root 4 = 2
6. multiply 2 * 2 which equals 4 in the denominator. Voila you're done!

Thanks a lot @potent lava and @wild turtle . I clearly understand the concept much better right now.

[potent lava]

i hope you can apply this to many examples now

understanding > memory

[restive otter]

Yes, got many of them ahead!! 🙂

[restive otter]

Ill firstly, definetly gonna understand the why video as you said

thanks a lot again!! Human explanation >>> AI explanation (as for now)

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