surds

[feral umbra]

use the difference of two squares

a^2 - b^2 = (a+b)(a-b)

[teal trellis]

One sec

[candid reef]

what

[candid reef]

how

how is 4 root 3 - 4 root 3= 8 root 3

[teal trellis]

I didn’t do that

[candid reef]

what did u do

[teal trellis]

Do u want me to show the solving steps

[feral umbra]

it’s much easier to use difference of two squares

[feral umbra]

it’s 4root3 - - 4root3

[feral umbra]

youve written it a bit wrong

[teal trellis]

Which one

[feral umbra]

when you did the left bit minus the right bit

[teal trellis]

I simplified it

[candid reef]

why is it --

[feral umbra]

you should have made the -4root3 into +4root3 since you minused a minus

[feral umbra]

you’re doing the left minus the right

[candid reef]

ohhhh yeahhh

[feral umbra]

(x + y) - (a - b) = x + y - a + b

you minus the minus b making it positive

[candid reef]

why is it not 7--7 then

[teal trellis]

I did it right lol

[feral umbra]

because the 7 is positive on the right hand side

[feral umbra]

you got the right answer but your penultimate line of working is incorrect

it should read ‘7 + 4sqrt3 - 7 + 4sqrt3’

[feral umbra]

if you just looked at the second to last line it would simplify to 0

[teal trellis]

No it wouldn’t

Because 4sq root 3 - - 4 sq root 4 = 4sq root 3 + 4 sq root 3

To give 8sqroot 3

[feral umbra]

yes but you didn’t put brackets around the right half

[candid reef]

oh

ok ig

ty

[teal trellis]

Ummm

Ur longing it out

[feral umbra]

bro

look at this

you should have always just used the difference of two squares

[teal trellis]

👍🏻

[candid reef]

wait

[teal trellis]

Can approach it 2 ways

Still get same answer at the end of the day don’t you

[candid reef]

4 root 3 is positive on the right aswell

[teal trellis]

It’s not

-4 root 3

[candid reef]

i meant

left

[teal trellis]

Yeah

[candid reef]

yeah

and its a minus 7 on the right

wait

[teal trellis]

No

[candid reef]

what am i saying

[feral umbra]

😭

[teal trellis]

LOOL

[candid reef]

basically

what i mean to say

why is it not 7 - - 7 aswell

if its 4 root 3 - - 4 root 3

[teal trellis]

Both 7s are positive so u do 7-7 not 7 - - 7

[feral umbra]

because the 7 on the right is positive but the 4root3 on the right is negative

[candid reef]

why did u write -7 then

[teal trellis]

Because we are subtracting

[feral umbra]

you should write 7 + 4root3 - (7 - 4root3)

otherwise technically that’s 0

[teal trellis]

Alright

[candid reef]

ohhh

waiy

i get it

[candid reef]

oh ok

also

one more thing

[feral umbra]

mhm

[candid reef]

what is rationalise

we never did it

[feral umbra]

so to rationalise the denominator of a fraction is to make there be no square roots on the bottom

[teal trellis]

When u have like a fraction surd

[candid reef]

yeah and how do u do that

[candid reef]

oh

thats so ez

[feral umbra]

you can then simplify that to 2root3

[teal trellis]

Yep

[feral umbra]

it gets a bit more complicated when there’s several terms on the bottom but oh well

[teal trellis]

Yeah

[candid reef]

ok..

anyway

are u allowed to divide everything by 3

[teal trellis]

Got to times by root 3

[candid reef]

ik im asking too much questions sry lol

it says simplify

[feral umbra]

urm not in the way you are thinking

[candid reef]

not rationalise

[feral umbra]

rationalising is a form of simplifying

[candid reef]

oh god

ty

ig

[feral umbra]

np

[candid reef]

there are so much things on the worksheet that we never done

wtf

[teal trellis]

What are they

[candid reef]

"show"

[feral umbra]

show what ?

[teal trellis]

U just got to show ur working basically

And get the answer

[candid reef]

proofs basically

[teal trellis]

Same thing basically

[candid reef]

oh

ok

i hate surds

[feral umbra]

proofs are a bit more rigorous but yeah

[candid reef]

a little bit

[candid reef]

uh

[feral umbra]

as in with proofs you HAVE to show ALL of your working and give reasons if it’s a circle theorem question wtc

[candid reef]

is that right

[teal trellis]

Here’s a solution for the first one u sent

[teal trellis]

Yes well done

[candid reef]

🥰

[candid reef]

so u basically js solve it

[teal trellis]

Yeah remembering to show all stages of ur working

[candid reef]

um

[teal trellis]

?

[candid reef]

do u multiply both brakets together or times them by root 11

in the numerator

[teal trellis]

Uhh

First I would do the double brackets

And times the product by root 11

[candid reef]

ok

thanks

[teal trellis]

Np

[candid reef]

sometimes in an exam i write 4×4=8 i hate when it happens to me

it happens sm aswell

[teal trellis]

Lool I’ve been there happens to the best of us

[candid reef]

fr

what is 2 root 3 × 2 root 3

is it just 6

[teal trellis]

12

[candid reef]

what

how

oh

[candid reef]

yeah

nvm

im js dumb

[teal trellis]

Dw

[teal trellis]

Think this just happened to u

[candid reef]

id be frustrated

imagine that was the reason u got an A instead of an A* in gcse💀😭

cz u did that and then messed up the whole question

[teal trellis]

Nahhh my biggest fear

[candid reef]

is that right

[candid reef]

why did u multiply by 2-root3

[teal trellis]

Got to do the opposite so if it’s + it becomes - vice Versa

It’s just a rule

[teal trellis]

And no it isn’t

Not sure how you got 62

[candid reef]

thats 12 lmao

but its cz i wrote 6 before it

[wise mica]

you wanna get rid of the surd and by multiplying by 2-rt3 you'll see you get two surds which cancel out

[teal trellis]

16-12 is 4

[candid reef]

omggg

how did my dumbass get 14

🤦‍♂️🤦‍♂️🤦‍♂️🤦‍♂️🤦‍♂️

[teal trellis]

Loooooll

[candid reef]

is that good

[wise mica]

yh

[teal trellis]

Lemme see

[wise mica]

i like how u just wrote 'shown' at the end

examiners arent blind lol

[candid reef]

😭

[feral umbra]

yep, make sure when you write 3-sqrt3/3-sqrt3 on the first stage you put the line between the numerator and denominator

[feral umbra]

it’s valid

or QED

[candid reef]

qed?

[wise mica]

qed?

[teal trellis]

qed?

[candid reef]

i think he meant qer

oh

"its a latin phrase

quod erat demonstrandum, meaning "which was to be demonstrated"."

[teal trellis]

Oh

[candid reef]

its quite goofy tbh lol

anyway

tysm

now what😭

them questions js keep getting wierder and harder😭

[rose yoke]

idk if im being stupid but

@candid reef

am i wrong?

[candid reef]

...

idk

maybe

[rose yoke]

pretty sure thats right tbf

[candid reef]

thats why im asking

cz idk the answer

😭

[rose yoke]

its right ye

[candid reef]

where did the 1/ root 2 go

[rose yoke]

if u times 1/root2 by root2 it should just be 1

[candid reef]

ok

what about the other root 2

[rose yoke]

root 2 times root 2 is just 2

[feral umbra]

it’s at the end of much much more formal proofs

[candid reef]

why did he add root 2/1

[feral umbra]

your method is good and valid

[wise mica]

helps with adding 1/rt2 + rt2

bc now you can make the denominators the same

[candid reef]

what

so what is the rule

what should u add

[wise mica]

its not exactly a rule

[candid reef]

omg

[wise mica]

u wanna write the 1/rt2 + rt2 as a single fraction

[candid reef]

so

how do i know what to add

in another question

[wise mica]

wdym

[candid reef]

how am i supposed to know what to add

[wise mica]

ur adding this

[candid reef]

how would that help u

[wise mica]

then u can do what's on the left

[candid reef]

ohh

so u need to make the denominator of 1/rt and rt2 the same

and add them

[wise mica]

exactly

and that would give you a single fraction

[candid reef]

yeahhhh

[wise mica]

so yk how to make the denoms the same?

[candid reef]

whats denoms

[wise mica]

denominator

[candid reef]

yeah

i learnt that in primary

[wise mica]

alr what would u do here

[candid reef]

umm

add rt2/1

and then

[wise mica]

so u can write rt2 as rt2/1

[candid reef]

multiply num and denom by rt 2

[wise mica]

yh

[candid reef]

to get a common denom

🥳

[wise mica]

now u got 1/rt2 + rt2 * rt2 / rt2 --> 1/rt2 + 2/rt2

3/rt2

so now we can write the original fraction as

1/3/rt2

[candid reef]

huh

[wise mica]

i just did this

to the rt2/1

[candid reef]

like that?

[wise mica]

yeah

[candid reef]

ok and then

[wise mica]

we can write the original thing as 1/3/rt2

[candid reef]

1/3/rt 2

yeah

which is basically the same as

[wise mica]

that basically says 1 divided by 3/rt2

[candid reef]

1*3/rt2

right?

[wise mica]

not quite

[candid reef]

...

[wise mica]

u didnt flip the fraction

[candid reef]

i meant to flip it

[wise mica]

alr then yh

[candid reef]

but i didnt

[wise mica]

1 * rt2/3

[candid reef]

so that is equal to

rt2/3

[wise mica]

yh

[candid reef]

🥳🥳

ill try the next one

[summer trout]

Somebody help@me with my post

[candid reef]

what do u do now