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yes. but i don't know how to apply this to work out the answer. please help me

you get 1

*now

\[\sqrt{12} + \sqrt{13}\] is bigger

I meant to say: you know (2) is bigger than (1)

yes. 2 is bigger than one so that makes \[\sqrt{13} - \sqrt{12}\] bigger?? :D

in that case x is bigger

imagine you had:\[x*4=1\]\[y*8=1\]which one would you say is bigger, x or y?

yes, x is bigger, therefore you know which one is bigger in your original question

yes i know \[\sqrt{13} - \sqrt{12}\] is bigger.

look back carefully through what was derived and re-think your answer.

yes!! i get it now. had to look at my solutions again using the different of 2 squares.

that makes \[\sqrt{12} - \sqrt{11}\] greater!

perfect! well done! :)

do you understand?

yeap...! i'm trying to do it on paper here :D

ok :)

and this shows \[\sqrt{12} - \sqrt{11}\] is bigger. you can see my working attached as an image

you expansion of \((\sqrt{11}+\sqrt{13})^2\) is not correct. remember that:\[(a+b)^2=a^2+2ab+b^2\]

so if i correct it. i get
\[48 ? 24 + 2\times \sqrt{13}\times \sqrt{11}\]

that is correct so far. now take the 24 to the left hand side and then divide both sides by 2

also remember that:\[\sqrt{a}\times\sqrt{b}=\sqrt{ab}\]

now i get (attached)

now the final answer!! :d

great! I'm glad you finally got there :)

perfect!

no problem at all my friend - the main thing here is you obviously love to learn! :)

he he - I love your "ambition" - keep up the good work! :)