extracting square roots

[untold pebble]

when you take a root of a fraction

\sqrt{\frac{x}{y}} = \frac{\sqrt{x}}{\sqrt{y}}

oops

$\sqrt{\frac{x}{y}} = \frac{\sqrt{x}}{\sqrt{y}}$

[topaz vapor]

taro

[untold pebble]

when you take the root of a fraction

you take the root of the numerator and the denominator

and ofc because its an equation

dont forget the pm

[pliant lava]

Thank you for this

[untold pebble]

all good

use .solved if your done

[pliant lava]

There's more

The 5,8,10

[untold pebble]

do you mind rotating it

[pliant lava]

uh

[untold pebble]

okay 5 8 and 10

question 5

isolate the t

[pliant lava]

Can you make like this

Like that format

[untold pebble]

wdym

[pliant lava]

Uh

[untold pebble]

u just wrote the same first two lines

and the last line

x^2 = 36

you can just write it as

sqrt(x^2) = sqrt(36)
x = 6, -6

[pliant lava]

teacher said that's the format

[untold pebble]

uh

that's a pre weird way

of formatting it

[pliant lava]

I don't understand it at all

[untold pebble]

its just weird

like

the first two lines are the same

then the last line is the same

like the 36 = 36 is not necessary

[pliant lava]

you know quadratic equation extracting square roots??

[untold pebble]

wdym

you can just send the question

[pliant lava]

This is the question

Number 5

[untold pebble]

question 5 aint quadratic equation extracing square roots

[pliant lava]

Whaat

What about the 8,10

[untold pebble]

8 and 10 yes

we can start with question 8 then

[pliant lava]

Alright

[untold pebble]

(w - 9)^2 = 12

first step is to get rid of the square

how do we do that

[pliant lava]

Idk

Bro

[untold pebble]

we need to isolate the w

[pliant lava]

Then

[untold pebble]

here let me explain it this way

if you had the equation

x + 3 = 5

what do you do

[pliant lava]

uh

[untold pebble]

you take the opposite operation

the opposite of addition is subtraction

so you subract 3 from both sides

x + 3 - 3 = 5 - 3

x = 5 - 3
= 2

[untold pebble]

now here

you have (w-9)^2

so we have to do the opposite operation

[pliant lava]

then

[untold pebble]

what's the opposite operatation of squaring

[pliant lava]

Opposite of addition is subtraction

fuck man

[untold pebble]

damn

uh

im thinking about how we can do this

here okay

you solved question 5, yes

[pliant lava]

how

[untold pebble]

wait

did u solve question 5

[pliant lava]

no

[untold pebble]

from the other worksheet

what

ok lets go all the way back to the start

$x^2 = 9$

[topaz vapor]

taro

[untold pebble]

what is x

[pliant lava]

x?

[untold pebble]

here

[pliant lava]

9?

[untold pebble]

no

x^2 = 9

if you said x is 9

your saying

9^2 = 9

81 = 9

?

[pliant lava]

oh yeah

square root of 81 is 9

[untold pebble]

but here

its x^2 = 9

so how do we

find x?

if i told you that

the opposite operation of squaring is squarerooting

would that help you

[pliant lava]

Uhh

[untold pebble]

damn

[pliant lava]

Dude

[untold pebble]

nono im thinking

okay lets try this

again

we got this

when u square a number, you multiply it by itself

correct?

like, $4^2 = 16$

[topaz vapor]

taro

[untold pebble]

@pliant lava correct?

[pliant lava]

Ye

[untold pebble]

great

now

to undo this operation

and find the original number

[pliant lava]

I'm in the bathroom bro

[untold pebble]

we take the squareroot

[pliant lava]

Wait hollon

[untold pebble]

alr

[pliant lava]

Back bro

So uh

[pliant lava]

How do we answer this

[untold pebble]

im not done

[untold pebble]

back to what i was saying

in order to find the original number

you take the squareroot

for example

if x^2 = 9

you take the squareroot of both sides

sqrt(x^2) = ±sqrt(9)

x = ±3

now for question 8

$(w - 9)^2 = 12$

[topaz vapor]

taro

[untold pebble]

now i said, in order to find the original number, we need to remove the square

by performing the opposite operation

meaning we have to?

[pliant lava]

About this

They told me it's

Fraction

[untold pebble]

what question?

aren't we doing question 8

[pliant lava]

Are you attempting to solve this problem?

[untold pebble]

ye he is

tryna explain the concept of completing the opposite operation

[pliant lava]

May I pose the solution?

[untold pebble]

i mean as long as you don't just give the solution

and walk through it w them

then yeah

[pliant lava]

1+1=1

[untold pebble]

???

bro it aint funny

[pliant lava]

Dued

[untold pebble]

fgs

[untold pebble]

sorry about them

we are talking about question 8, yes?

[pliant lava]

nah it's fine

yes

[untold pebble]

right

[pliant lava]

They said it's fraction

How do you do that

[untold pebble]

there arent

okay hm do you understand what i siad before

[pliant lava]

It's extracting Square roots but

Fraction

[untold pebble]

that in order to remove a square

you take the squareroot

x^2 = 9
you take the squareroot
x = ±3

you understand that concept correct?

[pliant lava]

Ye

[untold pebble]

okay back to (w-9)^2 = 12

because there's a square

we have to take the?

[pliant lava]

Square root

[untold pebble]

perfect

now when we take the squareroot

we will get

[pliant lava]

the

Have you considered getting rid of the exponent? For example: w-9 = +- surd 12

[untold pebble]

$w - 9 = \pm \sqrt{12}$

[topaz vapor]

taro

[pliant lava]

Then consider simplifying the square root 12

[untold pebble]

we're doing that

[untold pebble]

you understand this @pliant lava correct?

we took the root of both sides

[pliant lava]

Then the last step is solve for w by adding 9 to both sides

That's the thing I did

The format

[untold pebble]

alr lets take a look

wait this is a completely

different question

but okay

[pliant lava]

Yea

[untold pebble]

lemme take a look

4th line

whyd you write (s-4)^2 = 9

[pliant lava]

Final answer: w = 9 + 2surd3 and w = 9 - 2surd3

[pliant lava]

You change it so you can get the 13

The S is X

Did I make a slight error in my calculations?

But instead of X it's S

Idk

[untold pebble]

ye ik but

[pliant lava]

I did 4+9

[untold pebble]

(s-4)^2 - 81 = 0

(s-4)^2 = 81

then you took the root

s - 4 = 9

[pliant lava]

= 13

[untold pebble]

then you rewrote (s-4)^2 = 9

[pliant lava]

It's like

A shortcut

[untold pebble]

it's wrong

s - 4 = 9

that's correct

but writing (s-4)^2 = 9

is wrong

[pliant lava]

Both are incorrect I think

Whoops nvm I miss calculated

[untold pebble]

13 is a right solution

[pliant lava]

Ohh

[untold pebble]

however

-13 is incorrect

[pliant lava]

May I pose a math problem which has been hard for me to solve for a while?

Yes

You may

[untold pebble]

another help channel

[pliant lava]

Fair enough

[untold pebble]

13 is right, -13 is not

if you tried it

(s-4)^2 - 81 = 0

(s-4)^2 = 81

if you said s = -13

(-13-4)^2 = 81
(-17)^2 = 81
289 = 81

s = -13 is not a solution

[pliant lava]

But there's a 13

it's like

Positive and negative

[untold pebble]

13 is fine

(s-4)^2 = 81

s-4 = ±9

which means your solutions are

s - 4 = 9

s - 4 = -9

now if we add 4 to both solutions

s = 13

s = -5

understand now?

[pliant lava]

Where did you get the -5

Discord not giving me any notifications

[untold pebble]

u understood

this

correct

we got up to here

[pliant lava]

Ye

[untold pebble]

the plus or minus

means that the 9

is positive or negative

so we have

s - 4 = 9, and s - 4 = **-**9

[pliant lava]

yea

[untold pebble]

understood?

then just solve like normal

[pliant lava]

But where did you get -5

[untold pebble]

for s - 4 = 9

we added 4

s = 13

then for the other one

s - 4 = -9

we add 4 again

s = -9 + 4

s = -5

[pliant lava]

oh minus

[untold pebble]

yup

then u can plug it in to test

(s-4)^2 = 81

(-5 - 4)^2 = 81

(-9)^2 = 81

81 = 81

✅

[pliant lava]

Ohhh

And now

[untold pebble]

now..

?

[pliant lava]

How do we solve this

Using that format

[untold pebble]

which question

[pliant lava]

5,8,10

[untold pebble]

right again sorry

[pliant lava]

no It's okay

[untold pebble]

5

t + 4/7 = 5

we isolate the t

[pliant lava]

then its

5 + 4/7?

[untold pebble]

minus

opposite of addition is subtraction

[pliant lava]

oH

[untold pebble]

ye

so subract

t = 5 - 4/7

[verbal jasper]

t=31/7

[untold pebble]

mhm

[pliant lava]

31 what

how

[verbal jasper]

we can start by isolating the variable T. Subtracting 4/7 from both sides of the equation, we get T = 5 - 4/7. To simplify this, we need to find a common denominator for 5 and 4/7, which is 7. So, T = (35/7) - (4/7), which simplifies to T = 31/7. Therefore, the solution to the equation is T = 31/7.

[pliant lava]

Ooh

[untold pebble]

in other words

5 - 4/7

same denominator

5 = 35/7

35/7 - 4/7 = 31/7

[pliant lava]

Tbh I understand nothing

l0l

[untold pebble]

what dont u get

[pliant lava]

This

[untold pebble]

u understand this right

[pliant lava]

no

Therefore,

You determine the closure of vector A with the systematic evaluation

[untold pebble]

we had t + 4/7 = 5

and you subtracted both sides by 4/7

so you got t = 5 - 4/7

[pliant lava]

Ooh

[untold pebble]

then

in order to add and subtract fractions

they must have the same..?

[pliant lava]

Yes

[untold pebble]

same what

if i said to you

2/3 - 1/3

you would get 1/3

but if i said to you

2/4 - 1/3

you can't do the same thing

[pliant lava]

Olh

[untold pebble]

because the denominators are not?

[pliant lava]

Thank you for help bro

But I gotta sleep

[pliant lava]

,help

[topaz vapor]

A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!

[untold pebble]

u need help w a question?

[pliant lava]

yes

But you need to do a quadratic formula

[untold pebble]

send

[untold pebble]

can u rotate it

[untold pebble]

oh its the same one from yesterday

which one

[pliant lava]

1

And

[untold pebble]

1 isnt a quadratic

[pliant lava]

5,6

[untold pebble]

for 1 just bring the 12 over

x + 12 = 17

opposite operation is subtraction

so subtract 12 from both sides

[pliant lava]

You need to find the x thing

[untold pebble]

ye

ik

to find x

you have to isolate it

its just a one step equation

x + 12 = 17

all u need to do is make the x by itself

[pliant lava]

oh

Like

That

[untold pebble]

thats a completely different question tho

[pliant lava]

It's not

[untold pebble]

mate ur question was x + 12 = 17

but x^2 - 2x = 3

sure we can do that

[pliant lava]

Wait wait

no

The pic I send is the wrong one

[untold pebble]

alr that's fine

so are you familiar with the quadratic formula?

[pliant lava]

That

1,5,6

[untold pebble]

okay question 1

are you familiar with this form of a quadratic

$ax^2 + bx + c = 0$

[topaz vapor]

taro

[pliant lava]

uh

A lil

[untold pebble]

alright

do you know the quadratic formula?

[pliant lava]

no

[untold pebble]

alright

so the quadratic formula is the formula used to solve for x for quadratic equations

our first step

[untold pebble]

is to turn our equation

into this

you have $x^2 - 2x = 3$

[pliant lava]

Mhm

[topaz vapor]

taro

[untold pebble]

you need to get it in the form $ax^2 + bx + c = 0$

[topaz vapor]

taro

[untold pebble]

how do we do that

we need to make the right hand side equal to 0

[pliant lava]

Yes

[untold pebble]

so what do we do

to make that

[pliant lava]

uhh

We

[untold pebble]

we have 3 and we need to make it 0

[pliant lava]

we do

[untold pebble]

so what can we

do

to make the right hand side equal to 0

[pliant lava]

That

= 0

[untold pebble]

good

and do you know why

or did you just check google

[pliant lava]

nah

[untold pebble]

so how did u make it go from 3 to 0

[pliant lava]

i moved the 3

to make it like standard form

[untold pebble]

good

but like you know what you're technically doing right?

like when you say your moving

[pliant lava]

yes

[untold pebble]

it from the right to the left

your subtracting by 3

[pliant lava]

to

[untold pebble]

anyway

so now we're in the standartd form

[pliant lava]

x^2 is always 1 right??

[untold pebble]

$x^2 - 2x - 3 = 0$

[topaz vapor]

taro

[pliant lava]

when identifying

the abc

[untold pebble]

no

[pliant lava]

what

[untold pebble]

a and b are the coefficients

of x

c is just the constant

so if i gave you the equation $2x^2 + 9x - 1 = 0$

[topaz vapor]

taro

[untold pebble]

a = 2
b = 9
c = -1

understand?

[pliant lava]

uhh

[untold pebble]

$ax^2 + bx + c = 0$

[topaz vapor]

taro

[untold pebble]

$2x^2 + 9x - 1 = 0$

[pliant lava]

why on google its 1

[topaz vapor]

taro

[untold pebble]

do you see the resemblance

[untold pebble]

ye in our current question

its 1

but your asking if it will always be 1

not all equations will a be equal to 1

[pliant lava]

oh

[untold pebble]

remember that if its $x^2$, you have the invisible 1 as $x^2 = 1x^2$

[topaz vapor]

taro

[pliant lava]

ooh

[untold pebble]

anyway back to the equation $x^2 - 2x - 3 = 0$

[topaz vapor]

taro

[untold pebble]

we will use the quadratic formula now

so what is our a, b, and c

[pliant lava]

a = 2
b = 9
c = -1

[untold pebble]

no sorry i meant in our

original equation

[pliant lava]

a = 1
b = -2
c = -3

that

Hi

[untold pebble]

great

[pliant lava]

I see you guys are still solving this :))

[untold pebble]

now we will insert it into the quadratic formula

[untold pebble]

diff question

[pliant lava]

Ohh ok 👌

[untold pebble]

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

[topaz vapor]

taro

[pliant lava]

Quadratic formula

bro

[untold pebble]

now insert the values for a b and c

$x=\frac{-(-2)\pm\sqrt{(-2)^2-4(1*-3)}}{2(1)}$

[topaz vapor]

taro

[untold pebble]

following?

[pliant lava]

wait

[pliant lava]

is the -b is for my b = -2?

like

[untold pebble]

ye its a double negative

[pliant lava]

you put the -2 there

[untold pebble]

beacuse ur b is already negative

but the formula is -b

so you have - (-2)

[pliant lava]

alr

[untold pebble]

does that make sense?

[pliant lava]

yes

[untold pebble]

great

now lets simplify

start w the numerator

$-(-2)\pm\sqrt{(-2)^2-4(1*-3)}$

[pliant lava]

hm

[topaz vapor]

taro

[pliant lava]

im writing it

[untold pebble]

SURE

sure*

lemme know what u got

[pliant lava]

about this

why is there b^2

[untold pebble]

that's just how the formula is derived

i doubt you'd want the explanation of where the formula comes from

so

[pliant lava]

wait

[untold pebble]

good

now simplify

[pliant lava]

how do we simplify

[untold pebble]

well simplify the numerator

[pliant lava]

evaluate?

[untold pebble]

start from left to right

what's -(-2)

[pliant lava]

its the

uh

is it wrong

[untold pebble]

nono i mean

what is --2

[pliant lava]

cus if the -b

of

[untold pebble]

no i literally mean

what does it turn into

[pliant lava]

postive 2

i evaluated it

[untold pebble]

good

remember two negatives make a positive

now evalulate everything inside the root

[untold pebble]

why 4-44*1(-3)

[pliant lava]

I solved it

how

I think…

??

[untold pebble]

ye but let him

try to solve

[untold pebble]

you have 44

[pliant lava]

its 4 - 4

then the dot then 1

[untold pebble]

no

you wrote 4-44 * 1(-3)

[pliant lava]

no

wait hold on

[pliant lava]

oh i did

my bad

[untold pebble]

no worries

[pliant lava]

it should be 4 - 4 dot then 1

then (-3)

[untold pebble]

mhm

now evalulate

[pliant lava]

multiply?

i remember is uh

evaluate after evaluate multiply then add numbers

after that

evaluate the square root

then multiply the numbers

[untold pebble]

$2\pm\sqrt{4-4(1*-3)}$

[topaz vapor]

taro

[untold pebble]

this is ur numerator so far

do ur multiplication first

[pliant lava]

how did you get the (1 * - 3)

[untold pebble]

4ac

[untold pebble]

u also got that

[pliant lava]

ah so like

the 1 outside

[untold pebble]

i mean its the same

it doesnt matter

because ur multiplying all 3 terms

like

$2 * 3 * 4$ is the same as $3 * 4 * 2$ for example

[topaz vapor]

taro

[untold pebble]

doesnt matter the order for multiplication

since all terms will get multiplied anyway

[pliant lava]

ohh

[untold pebble]

anyway

1 * -3 is?

[pliant lava]

12

??

[untold pebble]

oh ur doing all 3

okay

4 * 1 * -3 is

?

not 12

[pliant lava]

wha

[untold pebble]

4 * 1 * -3

[pliant lava]

i dont get it

[untold pebble]

4AC

4ac i mean

your a is 1

ur c is -3

4 * 1 * -3

??

[pliant lava]

uhh

[untold pebble]

$4 * 1 * 3 = 12$

[topaz vapor]

taro

[untold pebble]

$4 * 1 * -3 = ?$

[topaz vapor]

taro

[pliant lava]

you multiplied it?

[untold pebble]

what

ye?

its 4 times a times c

4 * a * c

4ac

??

$2\pm\sqrt{4-(41-3)}$

[pliant lava]

so

[untold pebble]

this might make it easier to read

[pliant lava]

4 times 1 times 3?

[topaz vapor]

taro

[untold pebble]

4 * 1 * 3

is 12

but im asking

4 * 1 * -3

negative 3

[pliant lava]

then its -12?

yea negative 12

[untold pebble]

good

$2\pm\sqrt{4- (-12)}$

[topaz vapor]

taro

[untold pebble]

now 4--12

is?

[pliant lava]

yes

now

you make the 4 and 12 plus?

4 plus 12

= 16

[untold pebble]

great

$2\pm\sqrt{16}$

[topaz vapor]

taro

[untold pebble]

sqrt(16) is equal to?

[pliant lava]

yess

[untold pebble]

what is sqrt(16)

[pliant lava]

we use to evaluate the square root

the square root of 16 is 4

yea i finished it

[untold pebble]

sorry im back

yes

[untold pebble]

$\frac{2\pm4}{2}$

[pliant lava]

Check

[topaz vapor]

taro

[untold pebble]

looks great

well done

[pliant lava]

Thank you

How do i

Make this channel solved

[untold pebble]

just typed .solved

[pliant lava]

.solved