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how do i work out which number is greater?
(sqrt12  sqrt11), (sqrt13  sqrt12)
 one year ago
 one year ago
how do i work out which number is greater? (sqrt12  sqrt11), (sqrt13  sqrt12)
 one year ago
 one year ago

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asnaseerBest ResponseYou've already chosen the best response.1
@tomiko are you aware of this factorisation?\[a^2b^2=(a+b)(ab)\]
 one year ago

tomikoBest ResponseYou've already chosen the best response.1
yes. but i don't know how to apply this to work out the answer. please help me
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
look at the first term:\[\sqrt{12}\sqrt{11}\]if you multiply this by \(\sqrt{12}+\sqrt{11}\) what will you get?
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
correct. nor similarly multiply the second expression with \(\sqrt{13}+\sqrt{12}\)  what do you get?
 one year ago

tomikoBest ResponseYou've already chosen the best response.1
for that too i get 1. but one is definately greater. cause when i use the calculate i get 2 different values, making one of the pairs greater than the other.
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
good. now, out these two terms, which one is bigger:\[1. \sqrt{12}+\sqrt{11}\]\[2.\sqrt{12}+\sqrt{13}\]
 one year ago

tomikoBest ResponseYou've already chosen the best response.1
\[\sqrt{12} + \sqrt{13}\] is bigger
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
good. so you now know that: a) x times (1) = 1 b) y times (2) = 1 and you know (2) is bigger than one. therefore what can you conclude about x and y?
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
I meant to say: you know (2) is bigger than (1)
 one year ago

tomikoBest ResponseYou've already chosen the best response.1
yes. 2 is bigger than one so that makes \[\sqrt{13}  \sqrt{12}\] bigger?? :D
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
no  in terms of x and y that I listed, x is being multiplied by a smaller number than y is being multiplied by, but both end up as 1. therefore is x or y bigger?
 one year ago

tomikoBest ResponseYou've already chosen the best response.1
in that case x is bigger
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
imagine you had:\[x*4=1\]\[y*8=1\]which one would you say is bigger, x or y?
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
yes, x is bigger, therefore you know which one is bigger in your original question
 one year ago

tomikoBest ResponseYou've already chosen the best response.1
yes i know \[\sqrt{13}  \sqrt{12}\] is bigger.
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
look back carefully through what was derived and rethink your answer.
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
remember that \(\sqrt{13}  \sqrt{12}\) was multiplied by the bigger number \(\sqrt{13} + \sqrt{12}\) to get 1.
 one year ago

tomikoBest ResponseYou've already chosen the best response.1
yes!! i get it now. had to look at my solutions again using the different of 2 squares.
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
we showed that:\[(\sqrt{12}\sqrt{11})(\sqrt{12}+\sqrt{11})=1\]\[(\sqrt{13}\sqrt{12})(\sqrt{13}+\sqrt{12})=1\]and\[\sqrt{13}+\sqrt{12}\gt\sqrt{12}+\sqrt{11}\]
 one year ago

tomikoBest ResponseYou've already chosen the best response.1
that makes \[\sqrt{12}  \sqrt{11}\] greater!
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
perfect! well done! :)
 one year ago

tomikoBest ResponseYou've already chosen the best response.1
i undertand now. thank you very much! but you have any idea about this approach? Purely algebra ? Place ? i/o =, > or <. sqrt(12)sqrt(11) ? sqrt(13)sqrt(12) 2sqrt(12) ? sqrt(11)+sqrt(13) 48 ? ... Can you continue ?
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
ok what this approach is doing is bringing together the two square roots of 12 and and then squaring both sides. so:\[(2\sqrt{12})^2=4*12=48\]now you just need to square the right hand side:\[(\sqrt{11}+\sqrt{13})^2=?\]
 one year ago

tomikoBest ResponseYou've already chosen the best response.1
yeap...! i'm trying to do it on paper here :D
 one year ago

tomikoBest ResponseYou've already chosen the best response.1
and this shows \[\sqrt{12}  \sqrt{11}\] is bigger. you can see my working attached as an image
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
you expansion of \((\sqrt{11}+\sqrt{13})^2\) is not correct. remember that:\[(a+b)^2=a^2+2ab+b^2\]
 one year ago

tomikoBest ResponseYou've already chosen the best response.1
so if i correct it. i get \[48 ? 24 + 2\times \sqrt{13}\times \sqrt{11}\]
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
that is correct so far. now take the 24 to the left hand side and then divide both sides by 2
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
also remember that:\[\sqrt{a}\times\sqrt{b}=\sqrt{ab}\]
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
that is correct  just one step left now  square both sides BTW: It is better to save your images as .png format if you can  they are smaller than .jpg files
 one year ago

tomikoBest ResponseYou've already chosen the best response.1
now the final answer!! :d
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
great! I'm glad you finally got there :)
 one year ago

tomikoBest ResponseYou've already chosen the best response.1
sorry for all the bother. thanks for the help. i finished high school 6 years ago and didn't do any math at all and now just started uni. it's going to be a little change for me. i'm doing computer science now. lots of math in my class!! but i love subject.
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
no problem at all my friend  the main thing here is you obviously love to learn! :)
 one year ago

tomikoBest ResponseYou've already chosen the best response.1
challenge** thank you very much once again. now any question like this that comes my way i will murder it!!
 one year ago

asnaseerBest ResponseYou've already chosen the best response.1
he he  I love your "ambition"  keep up the good work! :)
 one year ago
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