algebra | Mathematics | Page 1

versed wolfBOT Sep 30, 2023, 7:11 AM

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tulip cave Sep 30, 2023, 7:58 AM

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the general approach is to rationalise it first @snow tulip

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that is, make the denominator rational by multiplying both the numerator and denominator by the conjugate of the denominator

snow tulip Sep 30, 2023, 7:59 AM

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So let’s say there’s a number with the radical

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Like this

tulip cave Sep 30, 2023, 7:59 AM

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yep

snow tulip Sep 30, 2023, 7:59 AM

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Why do we bring the 5

tulip cave Sep 30, 2023, 7:59 AM

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wdym?

snow tulip Sep 30, 2023, 7:59 AM

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So like the root 3 is irrational right

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Why can’t we just multiply the root 3

tulip cave Sep 30, 2023, 8:00 AM

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yes

snow tulip Sep 30, 2023, 8:00 AM

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Why do we bring the 5 and the root 3

tulip cave Sep 30, 2023, 8:00 AM

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snow tulip Why can’t we just multiply the root 3

its because the denominator wont become rational with it alone

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what you CAN do is multiply by $\sqrt{3}+\sqrt{2}$

distant pythonBOT Sep 30, 2023, 8:00 AM

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wolfqz

tulip cave Sep 30, 2023, 8:00 AM

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but that too only in this case

snow tulip Sep 30, 2023, 8:00 AM

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I can times then

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Wait

tulip cave Sep 30, 2023, 8:02 AM

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?

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do you know what the conjugate means

snow tulip Sep 30, 2023, 8:05 AM

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It’s like you turn the - into a positive question

tulip cave Sep 30, 2023, 8:05 AM

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yess

snow tulip Sep 30, 2023, 8:06 AM

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So if it’s 5 square root 2 + 2 square root 3 we will write it as 5 square root 2 - 2 square root 3

tulip cave Sep 30, 2023, 8:06 AM

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when you multiply a binomial with its conjugate, u can use the a^2 - b^2 property

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this is why we multiply by that

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to square the numbers in order to eliminate the square roots

snow tulip Sep 30, 2023, 8:07 AM

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tulip cave to square the numbers in order to eliminate the square roots

Is it possible for us to do this together

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My first step would be simplifying the radicals

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Then timing them

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And then just dividing

tulip cave Sep 30, 2023, 8:08 AM

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yh uhh

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what do u mean by

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"timing them"

snow tulip Sep 30, 2023, 8:08 AM

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Multiply

tulip cave Sep 30, 2023, 8:08 AM

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oh

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yh

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u can do that

snow tulip Sep 30, 2023, 8:09 AM

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So this confuses me right

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It breaks the 5 and the -2 to divide it by 25

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Is there any other way to do it

tulip cave Sep 30, 2023, 8:09 AM

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um the 25 came from 75-50

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and it took 5 common in order to simplify it

snow tulip Sep 30, 2023, 8:10 AM

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The -10 square root 6

tulip cave Sep 30, 2023, 8:10 AM

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yes $-10\sqrt{6} = 5 \times -2\sqrt{6}$

snow tulip Sep 30, 2023, 8:10 AM

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It broke it as (5 x -2) square root 6

distant pythonBOT Sep 30, 2023, 8:10 AM

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wolfqz

tulip cave Sep 30, 2023, 8:11 AM

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he just used the reverse distributive property

snow tulip Sep 30, 2023, 8:11 AM

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distant python **wolfqz**

Yea but is there any other way to do this

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Like

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I sometimes forget this

tulip cave Sep 30, 2023, 8:11 AM

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to cancel out common factors?

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no

snow tulip Sep 30, 2023, 8:12 AM

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I don’t even know what I’m doing at this point

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So I did square root 2 x square root 3 = square root 9

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Breuh

tulip cave Sep 30, 2023, 8:13 AM

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how did u get the - 150 in the denominator

snow tulip Sep 30, 2023, 8:13 AM

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Uhm

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Oh yea so

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5x5 = 25 + 2x3 = 6. 25x6 = 150

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Oh wait

tulip cave Sep 30, 2023, 8:14 AM

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umm

snow tulip Sep 30, 2023, 8:14 AM

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Uhm

tulip cave Sep 30, 2023, 8:15 AM

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$\left(5\sqrt{3}\right)^2 - \left(5\sqrt{2}\right)^2 = 25 \times 3 - 25 \times 2 = 25$

distant pythonBOT Sep 30, 2023, 8:15 AM

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wolfqz

tulip cave Sep 30, 2023, 8:15 AM

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youre supposed to get 25 in the denominator

snow tulip Sep 30, 2023, 8:16 AM

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Don’t you like conguate

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Wait

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.

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.

tulip cave Sep 30, 2023, 8:16 AM

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yes

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the conjugate of $5\sqrt{3} - 5\sqrt{2}$ is $5\sqrt{3}+5\sqrt{2}$

distant pythonBOT Sep 30, 2023, 8:16 AM

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wolfqz

snow tulip Sep 30, 2023, 8:16 AM

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I’m good at monomial radicals but bionomials are confusing

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What do I need to work on

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Like practice

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I’ve been trying to study this for the whole day

tulip cave Sep 30, 2023, 8:17 AM

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just practice rationalisation questions

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uhh where u from?

snow tulip Sep 30, 2023, 8:17 AM

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Canada

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You?

tulip cave Sep 30, 2023, 8:18 AM

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wait lemme send some qs

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im india

snow tulip Sep 30, 2023, 8:18 AM

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Theek hai bhai

tulip cave Sep 30, 2023, 8:18 AM

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try rationalising these

snow tulip Sep 30, 2023, 8:21 AM

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Ummm

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@tulip cave

tulip cave Sep 30, 2023, 8:21 AM

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isnt it supposed to be root49 - root36 in the denominator

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but thats just equal to one

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so the final answer becomes root7+root6

snow tulip Sep 30, 2023, 8:22 AM

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Oh yea oh yea

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Not root

tulip cave Sep 30, 2023, 8:22 AM

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snow tulip Not root

in the numerator

snow tulip Sep 30, 2023, 8:22 AM

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It should be like this I beleive

tulip cave Sep 30, 2023, 8:23 AM

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tulip cave try rationalising these

try giving the full simplified answer to the second one

snow tulip Sep 30, 2023, 8:23 AM

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snow tulip It should be like this I beleive

Is this right

tulip cave Sep 30, 2023, 8:23 AM

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snow tulip It should be like this I beleive

uhh in the denominator its wrong

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uhh

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no

snow tulip Sep 30, 2023, 8:23 AM

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How

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You square root

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49 square root is 7

tulip cave Sep 30, 2023, 8:24 AM

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$\left(\sqrt{7}-\sqrt{6}\right)\left(\sqrt{7}+\sqrt{6}\right) = \sqrt{49}-\sqrt{36} = 7-6 = 1$

snow tulip Sep 30, 2023, 8:24 AM

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How is it minus

distant pythonBOT Sep 30, 2023, 8:24 AM

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wolfqz

tulip cave Sep 30, 2023, 8:24 AM

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snow tulip How is it minus

multiply it

snow tulip Sep 30, 2023, 8:24 AM

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Bro don’t we go like distributive way

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Like square root 7x7,7x6 and then square root 6x7 and 6x6

tulip cave Sep 30, 2023, 8:26 AM

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$\left(\sqrt{7}-\sqrt{6}\right)\left(\sqrt{7}+\sqrt{6}\right) = \sqrt{7 \times 7} + \sqrt{7 \times 6} - \sqrt{7 \times 6} - \sqrt{6 \times 6}$

distant pythonBOT Sep 30, 2023, 8:26 AM

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wolfqz

tulip cave Sep 30, 2023, 8:26 AM

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this is what we get doing it using distributivity

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its still $\sqrt{49} - \sqrt{36}$

distant pythonBOT Sep 30, 2023, 8:26 AM

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wolfqz

tulip cave Sep 30, 2023, 8:26 AM

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this is because $-\sqrt{6} \times \sqrt{6} = -\sqrt{36}$

distant pythonBOT Sep 30, 2023, 8:26 AM

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wolfqz

snow tulip Sep 30, 2023, 8:28 AM

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Wait wait

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It’s square root 3

tulip cave Sep 30, 2023, 8:28 AM

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the denominator has 2

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because 5-3 = 2

snow tulip Sep 30, 2023, 8:28 AM

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The denominator is 3

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Huh

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5-2?

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It’s 4

tulip cave Sep 30, 2023, 8:28 AM

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snow tulip The denominator is 3

root 25 = 5

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root 4 = 2

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oh youve written 4 oops

snow tulip Sep 30, 2023, 8:29 AM

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Bhai wo root 4 hai

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Yep

tulip cave Sep 30, 2023, 8:29 AM

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5-2 = 3

snow tulip Sep 30, 2023, 8:29 AM

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Yep yep

tulip cave Sep 30, 2023, 8:29 AM

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yeah

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try the third one

snow tulip Sep 30, 2023, 8:32 AM

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Is this right?

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@tulip cave

tulip cave Sep 30, 2023, 8:34 AM

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umm no

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u should get $\frac{\sqrt{7} + 2}{3}$

snow tulip Sep 30, 2023, 8:35 AM

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Huh

tulip cave Sep 30, 2023, 8:35 AM

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thats the answer^

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u multiply both numerator and denominator by root7 + 2

snow tulip Sep 30, 2023, 8:35 AM

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What did I do wrong

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I did

tulip cave Sep 30, 2023, 8:36 AM

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uhh lemme see

snow tulip Sep 30, 2023, 8:36 AM

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2root 7

tulip cave Sep 30, 2023, 8:36 AM

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oops sorry

snow tulip Sep 30, 2023, 8:36 AM

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Huh

distant pythonBOT Sep 30, 2023, 8:36 AM

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wolfqz

tulip cave Sep 30, 2023, 8:36 AM

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u cant multiply 2 and root7

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do the binomial multiplistion method

snow tulip Sep 30, 2023, 8:37 AM

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I did 1x2 and 1x square root 7

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Uhm

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Ohhh

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I did 1x2

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But I didn’t do 1x7

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I see

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Can I have a complex question @tulip cave

tulip cave Sep 30, 2023, 8:38 AM

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fine

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

distant pythonBOT Sep 30, 2023, 8:38 AM

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wolfqz

snow tulip Sep 30, 2023, 8:41 AM

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tulip cave fine

Do you have the answer

tulip cave Sep 30, 2023, 8:42 AM

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uhh lemme see

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hmm yes i do

snow tulip Sep 30, 2023, 8:42 AM

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Share

tulip cave Sep 30, 2023, 8:42 AM

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the answer or the solution?

snow tulip Sep 30, 2023, 8:42 AM

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tulip cave Sep 30, 2023, 8:42 AM

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umm

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isnt the denominator supposed to be 1

snow tulip Sep 30, 2023, 8:43 AM

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.

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I did it the long way how

tulip cave Sep 30, 2023, 8:43 AM

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remember this identity

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

distant pythonBOT Sep 30, 2023, 8:43 AM

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wolfqz

snow tulip Sep 30, 2023, 8:43 AM

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So it was - square root 4?

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BREUH

tulip cave Sep 30, 2023, 8:44 AM

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hmm

snow tulip Sep 30, 2023, 8:44 AM

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Is the rest right?

tulip cave Sep 30, 2023, 8:44 AM

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uh idk

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make the denominator correct

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and then share solution

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bc with th incorrect denominator i cant say if its right or wrong

snow tulip Sep 30, 2023, 8:45 AM

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I simplified the square root 9

tulip cave Sep 30, 2023, 8:45 AM

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ic

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yes it is correct

snow tulip Sep 30, 2023, 8:46 AM

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FINALLY

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what grade are you in

tulip cave Sep 30, 2023, 8:47 AM

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10

snow tulip Sep 30, 2023, 8:47 AM

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.

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I’m in grade 10 too bruh

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India’s math is wayyy to strong

#algebra