how do i solve this i got math exam soon

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[mental vessel]

hi

oh this is just rationalization

you have to make the denominator a rational numbers

i suppose youre familiar with the notion of rationals and irrationals?

[midnight quarry]

YESS but i kinda dont understand it

[mental vessel]

wdym

this particular thing?

its just tryna make the denominator of a fraction Rational

by whatever means possible (and efficient)

[midnight quarry]

I guess maths is difficult for me cause i hate it sm its so boring

i dont understand why i need this in the future

its not even important

[mental vessel]

Aight bro then fail yo test

🔥

[midnight quarry]

NO STOP

I NEED TO GET 100%

I ALREADY UNDERSTAND THE OTHER PARTS OF THE EXAM, ITS JUST THIS ONE THING

[rare parrot]

Basically when you rationalising the denominator

Let's say our denominator is sqrt(3)

We just multiply the denominator and numerator by the sqrt(3)

Such that the denominator is 3

@midnight quarry

[midnight quarry]

THANK YOU

IK THIS

BUT LIKE

omg idk how to explain in english sorry im german😭

[rare parrot]

I'll just give you a question

And do your workings

Till you fail

[midnight quarry]

okay

[rare parrot]

$\frac{7}{\sqrt{5}}$

[fleet pine]

Muus

[rare parrot]

Rationalise

[midnight quarry]

omg wth

okay wait

[midnight quarry]

uhh

3,1?

[rare parrot]

Uh no

I don't want the decimal estimation

I want the rationalised form

The topic which you've literally asked to cover

[midnight quarry]

I DONT UNDERSTAND IT THATS THE THING

bro am hopeless when it comes to maths

[rare parrot]

Oh so

You don't understand

What the question be asking

[midnight quarry]

Yes

[rare parrot]

rationalise means to make the denominator of a surd rational

I mean not a formal definition

But for now let's take it as that

Do you know what a rational number is

[midnight quarry]

yes i know that

[rare parrot]

Ok

Is the sqrt(2) a rational number?

[midnight quarry]

no

i think

one sec

[rare parrot]

If it isn't a perfect square inside that sqrt

Then it's irrational

At least for the positive integers

Ok

So now that we've covered that

Let's say we had a fraction

$\frac{1}{\sqrt{2}}$

[fleet pine]

Muus

[rare parrot]

How can we make the denominator of this fraction rational

The numerator can become irrational

All that matters is that the denominator becomes rational

Recall
$(\sqrt{a})^2=a$

[fleet pine]

Muus

[midnight quarry]

uhh

wait wait wait

[midnight quarry]

yes i remember this

whenever the 2 is there

the number stays the same

[rare parrot]

Thats definitely one way of remembering it

[midnight quarry]

we call that small 2 hochzahl in german

[rare parrot]

Sure so

Any ideas how to rationalise the denominator?

[midnight quarry]

if im honest no😭

[rare parrot]

Is 2 a rational number?

[autumn lantern]

yes.

Definitely

[rare parrot]

Wowie

Would you bet your life on it

[autumn lantern]

yeah sure

[rare parrot]

Correcto

You keep your life

[midnight quarry]

.

[rare parrot]

What

[midnight quarry]

um

i mean yes

[autumn lantern]

it is of thr form p/q where q isnt 0. and p and q are coprimes

[rare parrot]

I think you might need to do some revision

[midnight quarry]

😭😭

[autumn lantern]

whats thr probelm u r getting

we might have a work around

[rare parrot]

Nah like bro's being asked to rationalise surds

But like

Bro does not know what rational means

[midnight quarry]

I DOTN GET THIS BRO

[autumn lantern]

aaah too many colour's

[midnight quarry]

this neither..

[midnight quarry]

UR RIGHT I DONT

idek what reellen is bro whats a reellen number

[rare parrot]

Alright

Let's go over some definitions

I'll just use some layman terms

A rational number is a number that can be expressed in the form p/q where p and q are integers

[midnight quarry]

what is p/q in german term

[rare parrot]

I mean do they have to be coprime @autumn lantern

[autumn lantern]

rational number is a number that can be expressed as p/q where in the simplest form p and q are coprimes and q is not 0

[autumn lantern]

in simplest form, yes.

[rare parrot]

Ah simplest form

[midnight quarry]

how r u both so smart

[rare parrot]

Well i think we can cut the coprime part

[midnight quarry]

om pg bro

[autumn lantern]

actually it's basically cuz of age difference

[rare parrot]

Yea

[midnight quarry]

how old r u

[autumn lantern]

16

[rare parrot]

15

[midnight quarry]

OKAY IM 15 TOO.

[rare parrot]

Off by 1😭

Oh then

Ripperoni

[autumn lantern]

i almost completed hs.

[rare parrot]

Anyways

A rational number is a number that can be expressed in the form p/q where p and q are integers

[autumn lantern]

and q≠0 for obv reasons

[midnight quarry]

integres is the whole number

right

like

ganze Zahl

..

[rare parrot]

Well whole numbers are the set of non negative integers

Integers include like -5,6,7

Negatives and positives

[autumn lantern]

whole numbers are all natural numbers with 0 combined

it is a subset of integers

[midnight quarry]

Ohh

[midnight quarry]

0,2,4,6

those are

straight numbers?😭

idk what yall call them in english

and "unstraight" numbers are numbers like 1,3,5,7

[rare parrot]

Even numbers

[rare parrot]

And odd number

German terminology is crazy

[autumn lantern]

whatever its called

basicallt rational numbers are numbers that can be expressed in thr form of p/q

whete p and w are normal positive and negative integers

like -1,-2 -3,-4 and 1,2,3,4 but not 0

[midnight quarry]

OHHH

[midnight quarry]

35/1

[autumn lantern]

rationalising focuses on making the denominator rational

[autumn lantern]

no

[midnight quarry]

ITS NOT RIGHT?

[autumn lantern]

no its not right

[midnight quarry]

am cryinG WHAT IS IT THEN

how do i calculate it

[rare parrot]

It's not a calculation it's more of like reforming the expression

Your objective is simply to make the denominator of the expression rational and simplify as best as possible from there

From example let's say I have

$\frac{1}{\sqrt{2}}$

[fleet pine]

Muus

[rare parrot]

To rationalise I simply re express the fraction with a rational denominator by multiplying the numerator and denominator by sqrt(2)

$\frac{1}{\sqrt{2}}=\frac{1\cdot\sqrt{2}}{\sqrt{2}\cdot\sqrt{2}}\newline = \frac{\sqrt{2}}{2}$

[fleet pine]

Muus

[rare parrot]

That's as far as we can simplify it

The rationalised form is sqrt(2)/2

[midnight quarry]

okay wait so

thats all?

[molten blaze]

is help still needed?

[midnight quarry]

what the hell

[midnight quarry]

yes pls

[molten blaze]

do you understand the basics?

[midnight quarry]

yes

[molten blaze]

okay, i’m going to let you try a tougher problem

[autumn lantern]

no.

[midnight quarry]

omg

[midnight quarry]

UM YES I DO

[molten blaze]

rationalize $\frac{\sqrt{2}}{\sqrt{3}-\sqrt{2}}$

[fleet pine]

dark matter

[autumn lantern]

as per me what they are considering basics is not same as ur basic

[midnight quarry]

Ohh

[molten blaze]

my basics is over one singular root.

[autumn lantern]

oh okay

[molten blaze]

like what denzio provided

[autumn lantern]

yeah then they r not confused

[molten blaze]

this is a bit tougher

[autumn lantern]

i remember when it was lockdown i bunked classes and a similar problem fucked me

[molten blaze]

i will have to introduce the concept of conjugate for this if you don’t understand

[midnight quarry]

the thing is i need an explanation on how to do it

[molten blaze]

alright, great

[autumn lantern]

u need to focus on making the denominator devoid of any underroots

[molten blaze]

so, let’s call an irrational number $\sqrt{a}+\sqrt{b}$

[fleet pine]

dark matter

[molten blaze]

it’s conjugate is denoted by $\sqrt{a}-\sqrt{b}$

[fleet pine]

dark matter

[autumn lantern]

pls reply with "yes" or "i understand" after every step, that helps a lot

[midnight quarry]

okay i know this one

[midnight quarry]

alright i will

[molten blaze]

this is the key here.

let’s say we’re given a fraction $\frac{1}{\sqrt{a}+\sqrt{b}}$

[fleet pine]

dark matter

[molten blaze]

what we want to do, to rid the denominator of irrational numbers, is multiply by $\frac{\sqrt{a}-\sqrt{b}}{\sqrt{a}-\sqrt{b}}$

[fleet pine]

dark matter

[molten blaze]

this is obviously equivalent to 1.

[autumn lantern]

@molten blaze sry to interupt but

[molten blaze]

?

[midnight quarry]

can you vc?

[autumn lantern]

isnt conjugate numbers, numbers having reciprocal equality with one another

[molten blaze]

maybe, but not right now

[midnight quarry]

i think its easier when you explain it in vc

[molten blaze]

i’ll try, then.

it’s not guaranteed, though

[strange bane]

Dark matter always helping

Love to see it

[autumn lantern]

or is it related by any kind of transformation?

[molten blaze]

in this case, i’m defining it similar to a complex conjugate

[autumn lantern]

oh

[molten blaze]

i just like to call them that way, it’s easier for my mind and probably most other people

[molten blaze]

anyway i’ll try to explain it here

[rare parrot]

They do call it conjugates in my country too

[molten blaze]

now one more key thing is to note that $(a+b)(a-b)=a^2-b^2$

[fleet pine]

dark matter

[molten blaze]

so now, let’s put this all together

[midnight quarry]

is this right?

[molten blaze]

we have $\frac{1}{\sqrt{a}+\sqrt{b}}\cdot\frac{\sqrt{a}-\sqrt{b}}{\sqrt{a}-\sqrt{b}}$

[fleet pine]

dark matter

[molten blaze]

no

[midnight quarry]

HUHHH

[molten blaze]

you got the right answer but have the wrong working.

you’re supposed to be multiplying using $\frac{\sqrt[3]{a^2}}{\sqrt[3]{a^2}}$

[autumn lantern]

is it righr

i doubt it

[molten blaze]

no, it’s right.

just the wrong working.

[autumn lantern]

wait was it just 1/cube root a

or the whole expression

[midnight quarry]

but doesnt the answer stay the same?

when its that

[fleet pine]

dark matter

[midnight quarry]

small 2 thing at the right top

[molten blaze]

no.

you fraction ends up being cbrt(a), which is not one

if i were your teacher i would not give you full marks for that

[midnight quarry]

😢

my teacher takes off half a point if i get it kinda wrong

[autumn lantern]

each step is evaluated

[molten blaze]

yeah, but conceptually it’s not clicking in your head

that’s where the marks are taken off

you have to make sure you’re multiplying by one

[autumn lantern]

u can modify the expression by multiplying and dividing tje same thing. u cant jusr change somethings value

[molten blaze]

from here we get that this is equal to $\frac{\sqrt{a}-\sqrt{b}}{a-b}$ because of the difference of squares mentioned earlier

[fleet pine]

dark matter

[midnight quarry]

english maths is so hard oh my goddd

[autumn lantern]

different terminology makes stuff hard

[midnight quarry]

im extremely used to german

[molten blaze]

i wish i knew german

heh, i only know math in spanish

[autumn lantern]

and i am very skeptical of each and every word because the exam i focused towards gets u using english

every word written in a question could make a difference

[midnight quarry]

IS THIS RIGHT

[molten blaze]

yes

[midnight quarry]

okay help me with this one

[rare parrot]

Dang do you not have a notebook app😭

[midnight quarry]

i do

[rare parrot]

Rationalising the denominator should be fairly obvious in this one

[midnight quarry]

i asked my dad for help but he said i should watch videos on youtube😢

[rare parrot]

Just ignore the numerator when coming up with the fraction equivalent to 1 to multiply by

[midnight quarry]

but then he scolds me if i get a bad grade on my exam

[midnight quarry]

i think i know how to solve that

[autumn lantern]

do the same thing u did earlier

there is only one term in tje denominator

[midnight quarry]

okay wait

[tight night]

<:closed:1306624376028004362> | Help Request Closed

This thread is being closed automatically as the starter message was deleted.

Nov 17, 2024, 3:46 PM

[twilit isle]

@midnight quarry

[midnight quarry]

aa

[twilit isle]

Alright but please don't delete the starter message

[molten blaze]

anyways.

[midnight quarry]

Okayyyy

[midnight quarry]

i think i understood it sm better now

[twilit isle]

Also, I am not sure that we will be able to close it properly afterwards

So ping me if we can't, I might have to delete this post

I hope you understand

[midnight quarry]

Its alright thank you

[molten blaze]

okay, can you try the example problem?

[twilit isle]

👍

[midnight quarry]

What was it again?

wb this @molten blaze @autumn lantern

[acoustic hull]

u just dont wanna understand

[autumn lantern]

ur method is correct

[acoustic hull]

sry mb

[autumn lantern]

the third one is wrong

[midnight quarry]

No its alright

[autumn lantern]

also write the multiplication sign in places u need it. u put = everywhere

even in places of multiplication sign

[midnight quarry]

do you mean this one?

[autumn lantern]

yes

it should be like 2 root (3) / 3

the denominator

[midnight quarry]

ohhh

OHHH

NOW I GET IT

[acoustic hull]

GGS

[midnight quarry]

FINALLY

omg

this exam will be ez

[acoustic hull]

Atb